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\begin{centering}
CAMERON UNIVERSITY\\
DEPARTMENT OF MATHEMATICS\\
LAWTON, OKLAHOMA 73505-6377, USA\\
\end{centering}

\vspace*{10pc}
\begin{centering}
CURRICULUM VITAE\\
$\qquad$\\
IOANNIS KONSTANTINOS ARGYROS\\
\end{centering}

\newpage
\noindent
1. {\bf PERSONAL}

\begin{tabbing}
PLACE OF BIRTH \quad \= Department of Mathematics \kill
NAME: \> Ioannis K. Argyros \\
\ \> \ \\
PLACE OF BIRTH:	\> Athens, Greece \\
\ \> \ \\
ADDRESS: \> Cameron University \\
\ \> Department of Mathematics \\
\ \> Lawton, OK 73505 USA\\
\ \> \ \\
E-MAIL: \> ioannisa@cameron.edu \\
\ \> \ \\
WEB PAGE: \> http://rattler.cameron.edu/swjpam/ia/ika.html\\
\ \> List of MR and CMP items: List of papers authored by Argyros, Ioannis, K.\\
\ \> http://www.ams.org/cgi-bin/author search=Argyros\\
\ \> \ \\
 FAX:	\> (580) 581-2616\\
\ \> \ \\
TELEPHONE: \> (580) 581-2908 or (580) 581-2481 (Office)\\
\ \> (580) 536-8754 (Home)\\
\end{tabbing}


\noindent
2. {\bf STUDIES}

\begin{tabbing}
PLACE OF BIRTH \quad \= Department of Mathematics \kill
(1) 1983--1984 \> Ph.D. in Mathematics \\
\ \> University of Georgia, Athens, Georgia\\
\ \> \ \\
(2) 1982--1983 \> M.Sc. in Mathematics\\
\ \> University of Georgia, Athens, Georgia\\
\ \> \ \\
(3) 1974--1979 \> B.Sc. in Mathematics \\
\ \> University of Athens, Greece
\end{tabbing}

\noindent
3. {\bf ACADEMIC EXPERIENCE}

\begin{tabbing}
PLACE OF BIRTH \quad \= Department of Mathematics \kill
(1) 1994--Present \> Full Professor, Cameron University, USA\\
\ \> \ \\
(2) 1993--1994 \> Tenured Associate Professor, Cameron University,
USA\\
\ \> \ \\
(3) 1990--1993 \> Associate Professor, Cameron University, USA\\
\ \> \ \\
(4) 1986--1990 \> Assistant Professor, New Mexico State
University, USA\\
\ \> \ \\
(5) 1984--1986 \> Visiting Assistant Professor, University of Iowa, USA\\
\ \> \ \\
(6) 1982--1984 \> Teaching-Research Assistant, University of
Georgia, USA\\
\ \> \ \\
(7) 1979--1982 \> Serving the Greek Army as a Technical
Consultant, Greece
\end{tabbing}

\newpage
\noindent
4. {\bf SCIENTIFIC ACTIVITY}

\medskip
\noindent
(A) {\bf Fields of Interest/Research Has Been Conducted In}:

\medskip
Numerical solution of ordinary - partial differential - integral -
functional equations on parallel computers; numerical methods; differential -
integral equations; numerical analysis; numerical functional
analysis; applied analysis; optimization; parallel computing;
fixed point theory; management science; wavelet and neural networks
and statistics.

\medskip
\noindent
(B) {\bf Editing}

\begin{enumerate}
\item[1.] I am the founder and Editor-in-Chief of the {\it Southwest Journal of Pure and
Applied Mathematics}. This is a peer-reviewed purely electronic journal established
in 1995 at Cameron University

web page: http://rattler.cameron.edu/swjpum/swjpam.html

\item[2.] Editor of the {\it Korean Journal of 
Computational and Applied Mathematics}
\item[3.] Editor of the Journal: {\it Computational Analysis and Applications}
(Plenum Publ.)

web page: http://www.wkap.nl/journalhome.html


\item[4.] Editor of the Journal: {\it Advances in Nonlinear Variational
Inequalities (ANVI)} (International Publications, USA)
\end{enumerate}


\noindent
(C) {\bf Book Reviewer}

\begin{enumerate}
\item[1.] {\it Elementary Numerical Analysis} by Kendall Atkinson, University of Iowa,
published in 1992 by John Wiley and Sons.
\item[2.] {\it Moduli of Continuity and Global Smoothness Preservation in
Approximation Theory}. Reviewed for Springer-Verlag
Publishers, World Scientific Publishing Company, Elsevier Science B.V., Birkhauser, and CRC Press,
1998.
\item[3.] {\it A Handbook on Analytic-Computational Methods and Applications}.
 Reviewed for Plenum Publ., Corp., World Scientific Publishing
Company, 1999.
\end{enumerate}
 

\noindent
(D) {\bf Scientific Papers Reviewer}

\medskip
I have reviewed a total of 158 papers for:

\begin{enumerate}
\item[1.] {\it Journal of Computational and Applied Mathematics}
\item[2.] {\it P.U.J.M.}
\item[3.] {\it  Mathematica Slovaca}
\item[4.] {\it Pure Mathematics and Applications (PUMA)}
\item[5.] {\it Southwest Journal of Pure and Applied Mathematics}
\item[6.] {\it IMA Journal of Numerical Analysis}
\item[7.] {\it Journal of Optimization Theory and Its Applications}
\item[8.] {\it Computer Physcis Communications}
\item[9.] {\it SIAM Journal Numerical Analysis}
\item[10.] {\it Computational and Applied Mathematics}, CAM 97, 98, 99,
Edmond, OK, USA
\item[11.] {\it Applied Mathematics Letters}
\item[12.] {\it Illinois Journal of Mathematics}
\item[13.] {\it Korean Journal of Computational and Applied Mathematics}
\item[14.] {\it Proceeding of the Cambridge Mathematical Society}
\item[15.] {\it Applicable Analysis}
\item[16.] {\it Journal of Applied Mathematics and Optimization}
\item[17.] {\it Computers and Mathematics with Applications}
\item[18.] {\it Computational and Applied Mathematics}
\item[19.] {\it Computational Analysis and Applications}
\item[20.] {\it Tamkang Journal of Mathematics}
\item[21.] {\it Soochow Journal of Mathematics}
\item[22.] {\it Portugaliae Mathematica}
\item[23.] {\it Aequationes Mathematicae}
\item[24.] {\it Advances in Nonlinear Variational Inequalities} (ANVI)
\item[25.] {\it Journal of Mathematical Analysis and Applications}
\item[26.] {\it Journal of Complexity}
\end{enumerate}

\medskip
\noindent
(E) {\bf Grants Received}

\begin{enumerate}
\item[1.] New Mexico State University Grant, (1986), \#1-3-43841, RC~\#87-01
\item[2.] New Mexico State University Grant, (1987), \#1-3-4-44770.
\item[3.] U.S.A.\ Army, (1988--1990), \#DAEA, 26-87-R-0013 (F.M.) Army (jointly
with the Mechanical Engineering Department at New Mexico State University).
Topic: ``Solution of differential equations on parallel computers"
\item[4.] Cameron University, Research support, July 1992, June 1998
\end{enumerate}

\medskip
\noindent
(F) {\bf Supervising Graduate Students}

\medskip
The following Ph.D.\ students have obtained their Ph.D.\ degree under my supervision: 
\begin{enumerate}
\item[1.] Losta Mansor, Ph.D.~dissertation title: Numerical Methods for Solving
Perturbation Problems Appearing in Elasticity and Astrophysics, 1989

\item[2.] Joan Peeples, Ph.D.~dissertation title: Point to Set Mappings and
Oligopoly Theory, 1989.
\end{enumerate}

\noindent
Member, Doctoral Examination Committee:
\begin{enumerate}
\item[3.] Aomar Ibenbrahim, Spring 1987
\item[4.] Maragoudakis Christos, Spring 1988
\newline
(Dean's Representative for both, Electrical Engineering Department)
\item[5.] Bellal Hossain, Fall 1996 University of Calcutta, India
\item[6.] Sri Pulak Guhathakurta, Spring 1998, University of Calcutta, India
\end{enumerate}

Chair, Master's Examination Committee
\begin{enumerate}
\item[7.] Mitra Ashan, Spring 1987
\item[8.] Christopher Stuart, Spring 1988
\item[9.] Anis Shahrour, Fall 1988
\end{enumerate}

\smallskip
Member, Master's Examination Committee
\begin{enumerate}
\item[10.] Juji Hiratsuka, Spring 1987 (Dean's Representative, Art
Department)
\item[11.] Alice Lynn Bertini, Spring 1988
\item[12.] Daniel Patrick Eshner, Summer 1989 (Dean's Representative,
Computer Science)
\end{enumerate}

\medskip
\noindent
(G) {\bf Committee Member for Hiring-Promotion-Tenure}

I have served as a committe member for:
\begin{enumerate}
\item[(a)] Hiring: Cameron University (USA), PUNJAB University (Pakistan)
\item[(b)] Promotion-Tenure: Cameron University (USA), Sultan Qaboos 
University, Sultanate of Oman, Sam Houston State University (USA)
\end{enumerate}

\medskip
\noindent
(H) {\bf Books and Monographs Published}

\begin{enumerate}
\item[1.] {\it The Theory and Applications of Iteration Methods}, CRC
Press, Inc., Systems Engineering Series, Boca Raton, Florida, 1993, Math.\
Rev.\ 65b:65001, Zbl.\ Math.\ 65J, 65052, (W.C.\ Rheinboldt (Pittsburgh)), 
(1992), 844--441, ISBN 0-8493-8014-6. (Textbook)
\item[2.] {\it A Unified Approach for Solving Nonlinear Operator Equations
and Applications}, West University of Timisoara, Department of Mathematics,
Mathematical Monographs, 62, Publishing House of the University of
Timisoara, Timisoara, 1997. (Monograph)
\item[3.] {\it The Theory and Application of Abstract Polynomial Equations},
St.\ Lucie/CRC/Lewis Publishers, Mathematics Series, Boca Raton, 
Florida, USA, 1998, ISBN 0-8493-8702-7. Springer-Verlag Publ., New York is
publishing this text since 2000 by taking over from CRC. (Textbook)
\item[4.] {\it Dictionary of Comprehensive Dictionary of Mathematics: Analysis, Calculus
and Differential Equations},
(Contributing Author) Chapman-Hall/CRC/Lewis Publishers, Boca Raton,
Florida, USA, 1999, ISBN: 0-8493-0320-6. (Textbook)
\item[5.] {\it Computational Methods for Abstract Polynomial Equations},
West University of Timisoara, Department of Mathematics,
Mathematical Monographs, 68, Publishing House of the University of
Timisoara, Timisoara, 1999. (Monograph)
\item[6.] {\it A Survey of Efficient Numerical Methods for Solving Equations and
Applications}, Kyung Moon Publishers, Seoul, Korea, 2000. (Textbook)
\item[7.] {\it A Unified Approach for Solving Equations, Part I:
On Infinite-Di\-men\-sional Spaces}, Handbook on Analytic Computational Methods
in Applied Mathematics, CRC Press, Inc., Boca Raton, Florida, 2000. (Monograph)
\item[8.] {\it A Unified Approach for Solving Equations, Part II:
On Finite-Di\-men\-sional Spaces}, Handbook on Analytic Computational Methods
in Applied Mathematics, CRC Press, Inc., Boca Raton, Florida, 2000. (Monograph)
\item[9.] {\it Two Contemporary Computational Aspects of Numerical
Analysis}, Applied Math. Reviews, Volume 1,  World Scientific
Publishing Comp., River Edge, NJ, 2000. (Monograph)
\item[10.] {\it Advances in the Efficiency of Computational Methods
and Applications}, World Scientific Publ. Co., River Edge, NJ, 2001.
(Textbook)
\end{enumerate}

{\bf Books and Monographs Under Preparation}
\begin{enumerate}
\item[11.] {\it Contemporary Computational Methods in Numerical Analysis,
Part I. Methods Involving Fr\'echet-Differentiable Operators of Order One}.
(Monograph)
\item[12.] {\it Contemporary Computational Methods in Numerical Analysis,
Part II. Methods Involving Fr\'echet-Differentiable Operators of Order 
$m$ $(m\geq 2)$}. (Monograph)
\item[13.] {\it Iterative Methods for Solving Equations Appearing in
Engineering and Economics}. (Textbook)
\end{enumerate}

\medskip
\noindent
(I) {\bf Research Articles}

\medskip
The scientific papers listed below have been published in the following
countries and at the top refereed journals in the following countries repeatedly:

\medskip
\noindent
{\bf America}: U.S.A., Brazil, Canada, Chile

\smallskip
\noindent
{\bf Europe}: U.K., Sweden, Belgium, Holland, Spain, Germany, Austria,
Hungary, Slovakia, Romania, Poland, Yugoslavia, Italy, Chech Republic

\smallskip
\noindent
{\bf Asia}: People's Republic of China, Republic of China, India, Pakistan,
Japan, Saudi Arabia, Korea, Singapore

\smallskip
\noindent
{\bf Australia}: Australia

\medskip
A 6\% of the scientific papers listed below have been published jointly
with Professors Mohammad Tabatabai (Cameron, USA), Dong Chen (University of
Arkansas, USA), Ferenc Szidarovszky (University of Arizona, USA), Losta
Mansor (Libya), Emil Catinas and Ion Pavaloiu (Romania).

\begin{enumerate}
\item[1.] A Contribution to the Theory of Nonlinear Operator Equations in Banach
Space, Master of Science Dissertation, 1983.
\item[2.] Quadratic Equations in Banach Space, Perturbation Techniques and 
Applications to Chandrasekhar's and Related Equations, Doctor of Philosophy
Dissertation, 1984.
\item[3.] Quadratic equations and applications to Chandrasekhar's and related
equations, {\it Bull. Austral. Math. Soc.}, Vol.\ 32, 2 (1985), 275--292;
{\it Not.\ Amer.\ Math.\ Soc.}, 85T-46-142; Z.F.M.6074063 (1987); Math. Rev.\ 87d:
Gerard Lebourg (Paris).
\item[4.] On a contraction theorem and applications, {\it Proc.\ Amer.\ Math.\
Soc., Symposium on Nonlinear Functional Analysis and Applications}, {\bf 45}, 1
(1986), 51--53; Math.\ Rev.\ 87h: 65108, Sh.~Singh, Z.F.M.6224077 (1988).
\item[5.] Iterations converging to distinct solutions of some nonlinear equations in
Banach space, {\it Internat.\ J.\ Math.\ \& Math.\ Sci.}, Vol.\ 9, No. 3 (1986),
585--587; Z.F.M.61447044 (1986); Math.\ Rev.\ 87j47097, P.P.\ Zabrejko (Minsk).

\item[6.] On the cardinality of solutions of multilinear differential equations
and applications, {\it Internat.\ J.\ Math.\ \& Math.\ Sci.}, Vol.\ 9, No.\ 4
(1986), 757--766; Math.\ Rev.\ 88e34017, Achmadjon Soleev (Samarkand); 
Z.F.M.66334008 (89), A.\ Soleev.

\item[7.] Uniqueness-Existence of solutions of polynomial equations in linear space,
{\it P.U.J.M.}, Vol.\ XIX (1986), 39--57; Z.F.M.62547050 (1988); Math.\ Rev.\
88g47116, B.G.\ Pachpatte (6-Mara).
\item[8.] On a theorem for finding ``large" solutions of multilinear equations in
Banach space, {\it P.U.J.M.}, Vol.\ XIX (1986), 29--37; Z.F.M.62547051 (1988); Math.\
Rev.\ 88g47115, B.G.\ Pachpatte (6-Mara).
\item[9.] On the approximation of some nonlinear equations, {\it Aequationes
Mathematicae}, {\bf 32} (1987), 87--95; Z.F.M.61447043 (1986); Math.\ Rev.\ 88g47124,
P.P.\ Zabrejko (Minsk).

\item[10.] An improved condition for solving multilinear equations, {\it P.U.J.M.},
Vol. XX (1987), 43--46; Math.\ Rev.\ 89c47065; Z.F.M.64747015, (1989).
\item[11.] On a class of nonlinear equations, {\it Tamkang J.\ Math.}, Vol.\
18, No.\ 2 (1987); 19--25; Math.\ Rev.\ 89f47091, Ramendra Krishna Bose
(1-SUNYF); Z.F.M.65347042, (1989), J.\ Appel.

\item[12.] On polynomial equations in Banach space, perturbations, techniques
and applications, {\it Internat.\ J.\ Math.\ \& Math.\ Sci.}, Vol. 10, No.\ 1 (1987),
69--78; Math.\ Rev.\ 88c47123, Heinrich Steinlein (Munich); Z.F.M.61747038, (1987).
\item[13.] A note on quadratic equations in Banach space, {\it P.U.J.M.}, Vol.
XX (1987), 47--50; Math.\ Rev.\ 89c47076; Z.F.M.64747016, (1989).
\item[14.] Quadratic finite rank operator equations in Banach space, {\it
Tamkang J.\ Math.}, Vol.\ 18, No.\ 4 (1987); 8--19; Z.F.M.66247011 (89); Math.\
Rev.\ 89k47100, Nicole Brillouet-Belluot (Nantes).

\item[15.] On some theorems of Mishra Ciric and Iseki, {\it Mat.\ Vesnik},
Vol.\ 39 (1987), 377--380; Math.\ Rev.\ 89c54083; Z.F.M.64854035, (1989).
\item[16.] An iterative solution of the polynomial equation in Banach space,
{\it Bull.\ Inst.\ Math.\ Acad.\ Sin.}, Vol.\ 15, No.\ 4 (1987), 403--410;
(Math.\ Rev.\ Author index 1989), 47H17, 46G99, 58C15.
\item[17.] A survey on the ideals of the space of bounded linear operators
on a separable Hilbert space, {\it Rev.\ Acad.\ Ci.\ Exactas Fis.\ Quim.\
Nat.\ Zaragoza}, II.\ Ser.\ 42 (1987), 24--43; Math.\ Rev.\ 89g47059.
\item[18.] On the solution by series of some nonlinear equations, {\it Rev.\
Acad.\ Ci.\ Exactas Fis.\ Quim.\ Nat.\ Zaragoza}, II.\ Ser.\ 42 (1987), 18--23;
Z.F.M.64947048, (1989); Math.\ Rev.\ 90f65085, V.V.\ Vasin (Sverdlosk).

\item[19.] Newton-like methods under mild differentiability conditions with
error analysis, {\it Bull.\ Austral.\ Math.\ Soc.}, Vol.\ 37, 1 (1988), 131--147;
Z.F.M.62965061, (1988), S.\ Reich; Math.\ Rev.\ 89b65142, A.V.\ Dzhishkariani
(Tbilisi).
\item[20.] On Newton's method and nondiscrete mathematical induction, {\it Bull.\
Austral.\ Math.\ Soc.}, Vol.\ 38 (1988), 131--140; Math.\ Rev.\ 90a65136, A.M.\
Galperin (Ben-Gurion Intern.\ Airp.).
\item[21.] On a class of nonlinear integral equations arising in neutron transport,
{\it Aequationes Mathematicae}, Vol.\ 35 (1988), 99--111; Math.\ Rev.\ 89M47058,
H.E.\ Gollwitzer (1-DREX).
\item[22.] On multilinear equations, {\it Pr.\ Rev.\ Mat.}, Vol.\ 14 (July 1988),
95--105.
\item[23.] New ways for finding solutions of polynomial equations in Banach
space, {\it Tamkang J.\  Math.}, Vol.\ 19, 1 (1988), 37--42; Math.\ Rev.\
90f47093, V.V.\ Vasin (Sverdlosk).
\item[24.] On a new iteration for solving the Chandrasekhar's H-equations,
{\it Pr.\ Rev.\ Mat.}, No.\ 15 (1988), 21--31.
\item[25.] On a new iteration for solving polynomial equations in Banach space,
{\it Funct.\ et Approx.\ Comment.\ Math.}, Vol.\ XIX (1988); Math.\ Rev.\
91d:65082, Xiaojun Chen.
\item[26.] Conditions for faster convergence of contraction sequences to the
fixed points of some equations in Banach space, {\it Tamkang J.\ Math.}, Vol.\
19, 3 (1988), 19--22; Math.\ Rev.\ 90j47074, Roman Manka (Mogilno).
\item[27.] On some nonlinear equations, {\it Pr.\ Rev.\ Mat.}, No.\ 15 (1988),
75--82.
\item[28.] On the approximation of solutions of compact operator equations,
{\it PR.\ Rev.\ Mat.}, Vol.\ 14, (July 1988), 29--46.
\item[29.] Approximating the fixed points of some nonlinear equations, {\it
Mathem.\ Slovaca}, {\bf 38}, No.\ 4 (1988), 409--417; Z.F.M.667 (1989), S.L.\
Singh. Math.\ Rev.\ 90g47109 (O.P.\ Kapoor (6--11TK)).
\item[30.] Some sufficient conditions for finding a second solution of the quadratic
equation in Banach space, {\it Mathem.\ Slovaca}, {\bf 4} (1988); Math.\ Rev.\
90g47108 (O.P.\ Kapoor (6--11TK)).
\item[31.] Concerning the approximation solutions of operator equations in
Hilbert space under mild differentiability conditions, {\it Tamkang J.\ Math.},
Vol.\ 19, No.\ 4 (1988), 81--87; Math.\ Rev.\ 91g:65137, P.S.\ Milojevic.
\item[32.] The Secant method and fixed points of nonlinear equations,
{\it Monatshefte fur Mathematik}, {\bf 106} (1988), 85--94; Z.F.M.65265043 (1989);
Math.\ Rev.\ 90b6511, A.M.\ Galperin, Ben-Gurion Intern.\ Airport.
\item[33.] An iterative procedure for finding ``large" solutions of the quadratic
equation in Banach space, {\it P.U.J.M.}, Vol.\ XXI (1988), 13--21; Math.\ Rev.\
91g:65136, P.S.\ Milojevic.
\item[34.] Vietta-Like relations in Banach space, {\it Rev.\ Acad.\ Ci.\
Exactas Fis.\ Quim.\ Nat.\ Zaragoza}, I, Ser.\ 43 (1988), 103--107;
Math.\ Rev.\ 47f47095, V.V.\ Vasin (Sverdlovsk).
\item[35.] A global theorem for the solutions of polynomial equations, {\it
Rev.\ Acad.\ Ci.\ Exactas Fis.\ Quim.\ Nat.\ Zaragoza}, I, Ser.\ 43 (1988),
93--101; Math.\ Rev.\ 90f47094, V.V.\ Vasin, (Sverdlosk).

\item[36.] Concerning the convergence of Newton's method, {\it P.U.J.M.},
Vol.\ XXI (1988), 1--11; Math.\ Rev.\ 91g:65135, P.S.\ Milojevic.
\item[37.] On the number of solutions of some integral equations arising in
radiative transfer, {\it Internat.\ J.\ Math.\ \& Math.\ Sci.}, Vol.\ 12, No.\ 2
(1989), 297--304; Math.\ Rev.\ 90h86004, S.\ Rajasekar (Ticuchirapalli).
\item[38.] On the approximate solutions of operator equations in Hilbert space
under mild differentiability conditions, {\it J.\ Pure \& Appl.\ Sci.}, Vol.\ 8,
No.\ 1 (1989), 51--56.
\item[39.] On the fixed points of some compact operator equations, {\it Tamkang J.\
Math.}, Vol.\ 20, No. 3 (1989), 203--209; Math.\ Rev.\ 91a47088, Jing Xian
Sum (PRC-Shan).
\item[40.] Error bounds for a certain class of Newton-like methods, {\it
Tamkang J.\ Math.}, Vol.\ 20, No.\ 4 (1989); Math.\ Rev.\ 91k:65096, J.W.\
Schmidt.
\item[41.] On a generalization of fixed and common fixed point theorems of
operators in complete metric spaces, {\it Rev.\ Mat.\ Cubo}, {\bf 5} (1989),
17--25.
\item[42.] Approximating distinct solutions of quadratic equations in Banach
space, {\it Rev.\ Mat.\ Cubo}, {\bf 5} (1989), 1--16.
\item[43.] Concerning the convergence of iterates to fixed points of nonlinear
equations in Banach space, {\it Bull.\ Malays.\ Math.\ Soc.}, Vol.\ 12, 2 (1989),
15--24; Math.\ Rev.\ Author index 1991.

\item[44.] A series solution of the quadratic equation in Banach space, {\it
Chinese J.\ Math.}, Vol.\ 27, No. 4 (1989); Math.\ Rev.\ 90k47131.
\item[45.] On a fixed point in a 2-Banach space, {\it Rev.\ Acad.\ Ciencias,
Zaragoza}, {\bf 44} (1989), 19--21; Math.\ Rev.\ 91a47077; Math.\ Rev.\ 91a:47077.
\item[46.] Some matrices in oligopoly theory, {\it New Mexico J.\ Sci.}, {\bf 29},
1 (1989), 22.
\item[47.] On a theorem of Fisher and Khan, {\it Rev.\ Acad.\ Ciencias,
Zaragoza}, {\bf 44} (1989), 13--17; Math.\ Rev.\ 91d:54048, Sehie Park.
\item[48.] On quadratic equations, {\it Mathematica-Rev.\ Anal.\ Numer. Theor.\
Approximation}, {\bf 18}, 1 (1989), 19--26; Math.\ Rev.\ 91f:47094.
\item[49.] Concerning the approximate solutions of nonlinear functional equations
under mild differentiability conditions, {\it Bull. Malays.\ Math.\ Soc.}, Vol.\
12, 1 (1989), 55--65; Math.\ Rev.\ 91k:47164, V.V.\ Vasin.
\item[50.] On the convergence of certain iterations to the fixed points of nonlinear
equations, {\it Annales sectio computatorica, Ann.\ Univ.\ Sci.\ Budapest.\
Sect.\ Computing}, {\bf 9} (1989), 21--31; Math.\ Rev.\ 91k:65095, J.W.\ Schmidt.
\item[51.] On the secant method and nondiscrete mathematical induction, {\it
Mathematica-Revue D'analyse Numerique et de theorie de l'approximation tome},
{\bf 18}, No.\ 1 (1989), 27--36; Math.\ Rev.\ 91j:65104.
\item[52.] On Newton's method for solving nonlinear equations and multilinear
projections, {\it Functiones et approximatio Comment.\ Math.}, {\bf XIX} (1990),
41--52; Math.\ Rev.\ 92b:4707, Joe Thrash.
\item[53.] Nonlinear operator equations and pointwise convergence, {\it Functiones
et approximatio Comment.\ Math.}, {\bf XIX} (1990), 29--39; Math.\ Rev.\ 92b:47106,
Joe Thrash.
\item[54.] Iterations converging faster than Newton's method to the solutions of
nonlinear equations in Banach space, {\it Functiones et approximatio Comment.\
Math.}, {\bf XIX} (1990), 23--28; Math.\ Rev.\ 91m:65164.
\item[55.] On some quadratic integral equations, {\it Functiones et Approximmatio},
{\bf XIX} (1990), 159--166; Math.\ Rev.\ 92d:47081, Aeinrich Steinlein.
\item[56.] A mesh independence principle for nonlinear equations using Newton's
method and nonlinear projections, {\it Rev.\ Acad.\ Ciencias.\ Zaragoza}, {\bf 45}
(1990), 19--35; Math.\ Rev.\ 92e:65076a, Mihai Turinci.
\item[57.] Error bounds for the modified secant method, {\it BIT}, {\bf 30} (1990),
92--100; Math.\ Rev.\ 91d:65083, Xiaojun Chen.
\item[58.] Improved error bounds for a certain class of Newton-like methods,
{\it J.\ Approximation Theory and its Applications}, (6:1) (1990), 80--98;
Math.\ Rev.\ 92a:65188, A.M.\ Galperin.
\item[59.] On the solution of some equations satisfying certain differential
equations, {\it P.U.J.M.}, Vol.\ XXIII (1990), 47--59; Math.\ Rev.\ 92d:65102.
\item[60.] On some projection methods for approximating the fixed points of
nonlinear equations in Banach space, {\it Tamkang J.\ Math.}, Vol.\ 21, 4 (1990),
351--357; Math.\ Rev.\ 92a:47072, Joe Thrash.
\item[61.] On some projection methods for the approximation of implicit
functions, {\it Appl.\ Math.\ Lett.}, Vol.\ 3, No.\ 2 (1990), 5--7; Math.\ Rev.\
91b65066.
\item[62.] On the monotone convergence of some iterative procedures in
partially ordered Banach spaces, {\it Tamkang J.\ Math.}, Vol.\ 21, No. 3
(1990), 269--277; Math.\ Rev.\ 91h:47067, Joe Thrash.
\item[63.] The Newton-Kantorovich method under mild differentiability conditions
and the Ptak error estimates, {\it Monatschefte fur Mathematik}, Vol.\ 109, No.\
3 (1990); Math.\ Rev.\ 91k:65034, J.W.\ Schmidt.
\item[64.] The secant method in generalized Banach spaces, {\it Appl.\ Math.\
\& Comput.}, {\bf 39} (1990), 111--121; Math.\ Rev.\ 91h:65099.
\item[65.] On the solution of equations with nondifferentiable operators and Ptak
error estimates, {\it BIT}, {\bf 30} (1990), 752--754; Math.\ Rev.\ 91k:65099.
\item[66.] On some projection methods for enclosing the root of a nonlinear
operator equation, {\it P.U.J.M.}, Vol.\ XXIII (1990), 35--46; Math.\ Rev.\
91h:47067, Joe Thrash.
\item[67.] A mesh independence principle for operator equations and their
discretizations under mild differentiability conditions, {\it Computing}, {\bf
45} (1990), 265--268; Math.\ Rev.\ 91i:65106.
\item[68.] On Newton's method under mild differentiability conditions, {\it
Arabian J.\ Math.}, Vol.\ 15, 1 (1990), 233--239; Math.\ Rev.\ 91k:65097, J.W.\
Schmidt.
\item[69.] Remarks on quadratic equations in Banach space, {\it Intern.\ J.\
Math.\ \& Math.\ Sci.}, Vol.\ 13, No.\ 3 (1990), 611--616; Math.\ Rev.\
91e:47062.
\item[70.] On the improvement of the speed of convergence of some iterations
converging to solutions of quadratic equations, {\it Acta Math.\ Hungarica},
Vol.\ 57/3-4 (1990), 245--252; Math.\ Rev.\ 93d:47121, Teodor Potra.
\item[71.] A note on Newton's method, {\it Rev.\ Acad.\ Ciencias Zaragoza},
{\bf 45} (1990), 37--45; Math.\ Rev.\ 92e:65076b, Mihai Turinici.
\item[72.] On the solution of compact linear and quadratic operator equations in
Hilbert space, {\it Rev.\ Acad.\ Ciencias Zaragoza}, {\bf 45} (1990), 47--52;
Math.\ Rev.\ 92e:65076c, Mihai Turinici.
\item[73.] On some generalized projection methods for solving nonlinear operator
equations with a nondifferentiable term, {\it Bull.\ Malays.\ Math.\ J.},
Vol.\ 13, No.\ 2 (1990), 85--91; Math.\ Rev.\ 92g:65065, Gerard, Lebourg.

\item[74.] Comparison theorems for algorithmic models, {\it Applied Math.\
and Comput.}, Vol.\ 40, No.\ 2 (Nov.\ 1990), 179--187; Math.\ Rev.\
92b:65102.
\item[75.] On an iterative algorithm for solving nonlinear equations, {\it Beitrage
zur Numerischen Math.} (Renamed Z.A.A.), Vol.\ 10, No.\ 1 (1991), 83--92;
Math.\ Rev.\ 93b:47132.
\item[76.] On time dependent multistep dynamic processes with set valued iteration
functions on partially ordered topological spaces, {\it Bull.\ Austral.\ Math.\
Soc.}, Vol.\ 43 (1991), 51--61; Math.\ Rev.\ 92d:65107, Tetsuro Yamamoto.
\item[77.] Error bounds for the secant method, {\it Math.\ Slovaca}, Vol.\ 41, 1
(1991), 69--82; Math.\ Rev.\ 92j:65086, K.\ Bohmer.

\item[78.] On the approximate solutions of nonlinear functional equations
under mild differentiability conditions, {\it Acta Math.\ Hungarica}, Vol.\
58 (1--2) (1991), 3--7; Math.\ Rev.\ Author index, 1992.
\item[79.] On the convergence of some projection methods with perturbation,
{\it J. Comput.\ and Appl.\ Math.}, {\bf 36} (1991), 255--258; Math.\ Rev.\
92f:65065, H.R.\ Shen.
\item[80.] On an application of a modification of the Zincenko method to the
approximation of implicit functions, {\it Z.A.A.}, {\bf 10} 3 (1991), 391--396;
Math.\ Rev.\ 93b:47133, Tetsuro Yamamoto.
\item[81.] On some projection methods for solving nonlinear operator equations
with a nondifferentiable term, {\it Rev.\ Academia de Ciencias, Zaragoza}, {\bf 46}
(1991), 17--24; Math.\ Rev.\ 92m:47133.
\item[82.] Integral equations for two-point boundary value problems, {\it Rev.\
Academia de Ciencias, Zara\-goza}, {\bf 46} (1991), 25--35; Math.\ Rev.\ 
93b:65205, Jan Pekar.
\item[83.] A fixed point theorem for orbitally continuous functions, {\it
Pr.\ Rev.\ Mat.}, Vol.\ 10, No. 7 (1991), 53--57; Math.\ Rev.\ 93d:47101, Ramendra
Krishna Bose.
\item[84.] Bounds for the zeros of polynomials, {\it Rev.\ Academia de
ciencias, Zaragoza}, {\bf 47} (1992), 61--66; Math.\ Rev.\ 94a:26035, N.K.\ Govil.
\item[85.] On a class of quadratic equations with perturbation, {\it Functiones
et Approximmatio}, {\bf XX} (1992), 51--63; Math.\ Rev.\ 94a:45011, P.M.\ Gupta.
\item[86.] On a new iteration for finding ``almost" all solutions of the quadratic
equation in Banach space, {\it Studia Scientiarum Mathematicarum Hungarica},
{\bf 27}, (3--4) (1992), 361--368; Math.\ Rev.\ 94d:65037, J.W.\ Schmidt.
\item[87.] A Newton-like method for solving nonlinear equations in Banach space,
{\it Studia Scientiarum Mathematicarum Hungarica}, {\bf 27} (3--4) (1992),
369--378; Math.\ Rev.\ 94d:65038, J.W.\ Schmidt.
\item[88.] On the convergence of nonstationary Newton methods, {\it Func.\ et
Approx.}, Vol.\ XXI (1992), 7--16; Math.\ Rev.\ 95g:65080, A.M.\ Galperin.
\item[89.] On an application of the Zincenko method to the approximation of
implicit functions, {\it Publicationes Mathematicae Debrecen}, Vol.\ 40/1--2
(1992), 43--49; Math.\ Rev.\ 93c:47076, A.M.\ Galperin.

 \item[90.] Improved error bounds for the modified secant method, {\it Intern.\
J.\ Computer Math.}, Vol.\ 43, No.\ 1+2 (1992), 99--109.
\item[91.] On the midpoint method for solving nonlinear operator equations in
Banach spaces, {\it Appl.\ Math.\ Letters}, Vol.\ 5, No.\ 4 (1992), 7--9; Math.\ Rev.\
96b:65061.
\item[92.] On an application of a Newton-like method to the approximation of implicit
functions, {\it Math.\ Slovaca}, {\bf 42}, No.\ 3 (1992), 339--347; Math.\ Rev.\
93h:65081, J.W.\ Schmidt.
\item[93.] On the monotone convergence of general Newton-like methods, {\it
Bull.\ Austral.\ Math.\ Soc.}, {\bf 45} (1992), 489--502; Math.\ Rev.\
93c:65077, A.G.\ Kartsatos.
\item[94.] Convergence of general iteration schemes, {\it J.\ Math.\ Anal.\ and
Applic.}, {\bf 168}, No.\ 1 (1992), 42--62; Math.\ Rev.\ 93d:65055, S.\ Sridhar.
\item[95.] Some generalized projection methods for solving operator equations,
{\it Journ.\ Comp.\ Appl.\ Math.}, {\bf 39}, No.\ 1 (1992), 1--6; Math.\ Rev.\
92m:65079.
\item[96.] Sharp error bounds for a class of Newton-like methods under weak
smoothness assumptions, {\it Bull.\ Austral.\ Math.\ Soc.}, {\bf 45} (1992),
415--422; Math.\ Rev.\ 93c:65076, A.G.\ Kartsatos.
\item[97.] Approximating Newton-like procedures, {\it Appl.\ Math.\ Lett.},
Vol.\ 5, No.\ 1 (1992), 27--29.
\item[98.] On a mesh independence principle for operator equations and the secant
method, {\it Acta Math.\ Hungarica}, {\bf 60}, 1--2 (1992), 7--19; Math.\ Rev.\
94g:65057, A.M.\ Galperin.
\item[99.] On the solution of quadratic integral equations, {\it P.U.J.M.},
Vol.\ XXV (1992), 131--143; Math.\ Rev.\ 95j:65177, P. Uba.
\item[100.] The secant method under weak assumptions, {\it Proceedings CAM 92},
Edmond, OK, (June 1992), 7--18.
\item[101.] On the convergence of generalized Newton-methods and implicit functions,
{\it Journ.\ Comp.\ Appl.\ Math.}, {\bf 43} (1992), 335--342; Math.\ Rev.\
93m:65076, J.W.\ Schmidt.
\item[102.] On a Stirling-like method, {\it P.U.J.M.}, Vol.\ XXV (1992), 83--94;
Math.\ Rev.\ 95j:65062, Anton Suhadolc.
\item[103.] An algorithm for solving nonlinear programming problems using
Karmarkar's technique, {\it Proceedings CAM 92}, Edmond, OK, (June 1992),
287--296.
\item[104.] On the approximate construction of implicit functions and Ptak error
estimates, {\it P.U.J.M.}, Vol.\ XXV (1992), 95--98; Math.\ Rev.\ Author Index 1995.
\item[105.] On the numerical solution of linear perturbed two-point boundary
value problems with left, right and interior boundary layers, {\it Arabian J.\
Science and Engineering}, {\bf 17}: 4B (October 1992), 611--624; Math.\ Rev.\
94c:65097.
\item[106.] On the convergence of Newton-like methods, {\it Tamkang J.\ Math.},
Vol.\ 23, No.\ 3 (1992), 165--170; Math.\ Rev.\ 93m:65077, J.W.\ Schmidt.
\item[107.] On the monotone convergence of algorithmic models, {\it Applied Math.\
and Comput.}, {\bf 48}, (2--3) (1992), 167--176; Math.\ Rev.\ 92m:47134, Vincentiu
Dumitru.
\item[108.] Approximating Newton-like iterations in Banach space, {\it P.U.J.M.},
Vol.\ XXV (1992), 49--59; Math.\ Rev.\ 95j:65061, Anton Suhadolc.
\item[109.] On the approximation of quadratic equations in Banach space using
finite rank operators, {\it Rev.\ Academia de ciencias Zaragoza}, {\bf 47} (1992),
67--76; Math.\ Rev.\ 94f:47085.
\item[110.] Remarks on the convergence of Newton's method under Holder continuity
conditions, {\it Tamkang J.\ Math.}, Vol.\ 23, No.\ 4 (1992), 269--277;
Math.\ Rev.\ 94b:65080, J.W.\ Schmidt.
\item[111.] On the solution of nonlinear operator equations in Banach space
and their discretizations, {\it Pure Mathematics and Applications}, Ser.\ B, Vol.\
3, No.\ 2--3--4 (1992), 157--173; Math.\ Rev.\ 94i:65069, C..\ Ilioi.
\item[112.] On the convergence of optimization algorithms modeled by
point-to-set mappings, {\it Pure Mathematics and Applications}, Ser.\ B, Vol.\
3, No.\ 2--3--4 (1992), 77--86; Math.\ Rev.\ 94i:90117, Han Ch'ing Lai.
\item[113.] On an application of a modification of a Newton-like method to the
approximation of implicit functions, {\it Bull.\ Malays Math.\ Soc.}, Vol.\ 16,
1 (1993), 25--32.
\item[114.] On the convergence of inexact Newton-like methods, {\it Public.
Math.\ Debrecen}, Vol.\ 43, 1--2 (1993), 79--85; Math.\ Rev.\ 94h:65064, Carl T.\
Kelley.
\item[115.] On some projection methods for the solution of nonlinear operator
equations with nondifferentiable operators, {\it Tamkang J.\ Math.}, Vol.\ 24,
No.\ 1 (1993), 1--8; Math.\ Rev.\ 94m:65097, A.V.\ Dzhishkariani.
\item[116.] An initial value method for solving singular perturbed two-point
boundary value problems, {\it Arabian Journ.\ Scienc.\ and Engineer.}, Vol.\ 18,
1 (1993), 3--5.
\item[117.] On the solution of nonlinear equations with a nondifferentiable
term, {\it Revue D'analyse Numerique et de theorie de l'approximation}, Tome 22,
2 (1993), 125--135; Math.\ Rev.\ 96a:65092, A.M.\ Galperin (IL-BGUN; Be'er Sheva).
\item[118.] Some methods for finding error bounds for Newton-like methods under
mild differentiability conditions, {\it Acta Math.\ Hungarica}, {\bf 61}, (3--4)
(1993), 183--194; Math.\ Rev.\ 94m:65096, A.V.\ Dzhishkariani.
\item[119.] On the secant method, {\it Publicationes Mathematicae Debrecen},
Vol.\ 43, 3--4 (1993), 223--238; Math.\ Rev.\ 95j:47077, R.\ Kodnar.
\item[120.] Improved error bounds for Newton's method under generalized
Zabrejko-Nguen-type assumptions, {\it Appl.\ Math.\ Letters}, Vol.\ 6, No.\ 3
(1993), 75--77; Math.\ Rev.\ Author index 1996.
\item[121.] A fourth order iterative method in Banach spaces, {\it Appl.\ Math.\
Letters}, Vol.\ 6, No.\ 4 (1993), 97--98; Math.\ Rev.\ Author index 1996.
\item[122.] Newton-like methods and nondiscrete mathematical induction,
{\it Studia Scientiarum Mathematicarum Hungarica}, {\bf 28} (1993), 417--426;
Math.\ Rev.\ 95b:47084, A.M.\ Galperin.
\item[123.] Robust estimation and testing for general nonlinear regression models,
{\it Appl.\ Math.\ and Comp.}, {\bf 58} (1993), 85--101; Math.\ Rev.\
94i:62097, Adrej Pazman.
\item[124.] A mesh independence principle for nonlinear operator equations in
Banach space and their discretizations, {\it Studia Scientiarum Math.\ Hung.},
{\bf 28} (1993), 401--415; Math.\ Rev.\ 95b:65077, A.M.\ Galperin.
\item[125.] Sharp error bounds for the secant method under weak assumptions,
{\it P.U.J.M.}, Vol.\ XXVI (1993), 54--62; Math.\ Rev.\ Author index 1995.
\item[126.] An error analysis of Stirling's method in Banach spaces, {\it Tamkang
J.\ Math.}, Vol.\ 24, No.\ 2 (1993), 115--133; Math.\ Rev.\ 94h:65058, A.M.\
Galperin.
\item[127.] New sufficient conditions for the approximation of distinct
solutions of the quadratic equation in Banach space, {\it Tamkang J.\ Math.},
Vol.\ 24, No.\ 4 (1993), 355--372; Math.\ Rev.\ 95f:47090.
\item[128.] On the convergence of inexact Newton methods, {\it Chinese J.\ Math.},
Sept.\ Vol.\ 21, No.\ 3 (1993), 227--234; Math.\ Rev.\ 94f:47088, Mihai Turinici.
\item[129.] On the solution of equations with nondifferentiable operators,
{\it Tamkang J.\ Math.}, Vol.\ 24, No.\ 3 (1993), 237--249; Math.\ Rev.\ 94i:65070,
C.\ Ilioi.
\item[130.] Sufficient conditions for the convergence of general iteration
schemes, {\it Chinese J.\ Math.}, Vol.\ 21, No.\ 2 (1993), 195--205; Math.\ Rev.\
94f:47087, Mihai Turinici.
\item[131.] On a two-point Newton method in Banach spaces of order four and
applications, (1993), Proceedings of the 9th Annual Conference on Applied
Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 34--48;
{\it P.U.J.M.}, Vol.\ 27 (1994), 23--33; {\it Rev.\ Academia de Ciencias,
Zaragoza}, {\bf 50} (1995), 5--13; Math.\ Rev.\ Author index 1996.
\item[132.] On a two-point Newton method in Banach spaces of order three and
applications, Proceedings of the 9th Annual Conference on Applied Mathematics,
CAM 93, University of Central Oklahoma, Edmond, (1993), 24--37; {\it P.U.J.M.},
Vol.\ 27 (1994), 10--22; Math.\ Rev.\ Author index 1996.
\item[133.] On a two point Newton-method in Banach spaces and the Ptak error
estimates, Proceedings of the 9th Annual Conference on Applied Mathematics, CAM
93, University of Central Oklahoma, Edmond, (1993), 8--24; {\it P.U.J.M.},
Vol. XXX, (1997); {\it Communications on Applied Nonlinear Analysis},
7, (2000), 2, 87--100.
\item[134.] Sufficient convergence conditions for iteration schemes modeled by
point-to-set mappings, Proceedings of the 9th Annual Conference on Applied
Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 48--52.
Also {\it Applied Mathematics Letters}, Vol.\ 9, No.\ 2 (1996), 71--73;
Math.\ Rev. Author index 1996.
\item[135.] On the convergence of a Chebysheff-Halley-type method under
Newton-Kantorovich hypotheses, {\it Appl.\ Math.\ Letters}, Vol.\ 6, No.\ 5
(1993), 71--74; Math.\ Rev.\ Author index 1996.
\item[136.] On an application of a variant of the closed graph theorem and
the secant method, {\it Tamkang J.\ Math.}, Vol.\ 24, No.\ 3 (1993), 251--267;
Math.\ Rev.\ 94m:65098, Rabindra Nath Sen.
\item[137.] Newton-like methods in partially ordered Banach spaces,
{\it Approx.\ Theory and Its Applic.}, {\bf 9}:1 (1993), 1--9; Math.\ Rev.\
94f:47086, Mihai Turinici.
\item[138.] Results on the Chebyshev method in Banach spaces, {\it
Proyecciones Revista}, Vol.\ 12, No.\ 2 (1993), 119--128; Math.\ Rev.\ 94j:65078,
A.M.\ Galperin (IL-BGUN; Be'er Sheva).
\item[139.] On the convergence of an Euler-Chebysheff-type method under
Newton-Kantorovich hypotheses, {\it Pure Mathematics and Applications}, Vol.\
4, No.\ 3 (1993), 369--373; Math.\ Rev.\ 95g:65081, Tetsuro Yamamoto.
\item[140.] A note on the Halley method in Banach spaces, {\it Appl.\ Math. and
Comp.}, {\bf 58} (1993), 215--224; Math.\ Rev.\ 94k:65082, Erich Bohl (Konstanz).
\item[141.] On the solution of underdetermined systems of nonlinear equations in
Euclidean spaces, {\it Pure Mathematics and Applications}, Vol.\ 4, No.\ 3 (1993),
199--209; Math.\ Rev.\ 95a:65089.
\item[142.] On the a posteriori error bounds for a certain iteration under
Zabrejko-Ngyen assumptions, {\it Rev.\ Academia de Ciencias, Zaragoza}, {\bf 48}
(1993), 77--85; Math.\ Rev.\ 95b:65076.
\item[143.] Newton-like methods in generalized Banach spaces, {\it Functiones
et Approximatio}, {\bf XXII} (1993), 107--114; Math.\ Rev.\ 95i:65088, Mihai
Turinici.
\item[144.] On S-order of convergence, {\it Rev.\ Academia de Ciencias Zaragoza},
{\bf 48} (1993), 69--76; Math.\ Rev.\ Author index 1994.
\item[145.] A theorem on perturbed Newton-like methods in Banach spaces,
{\it Studia Scientiarum Mathematicarum Hungarica}, {\bf 29} (1994), 295--305;
Math.\ Rev.\ 95i:65089.
\item[146.] Some notes on nonstationary multistep iteration processes, {\it Acta
Mathematica Hungarica}, Vol.\ 64, 1 (1994), 59--64; Math.\ Rev.\ 94m:90098.
\item[147.] Improved a posteriori error bounds for Zincenko's iteration, {\it Intern.
J.\ Comp.\ Math.}, Vol.\ 51 (1994), 51--54.
\item[148.] The Jarratt method in a Banach space setting, {\it J. Comp.\ Appl.\
Math.}, {\bf 51} (1994), 103--106; Math.\ Rev.\ 95c:65088.
\item[149.] The midpoint method in Banach spaces and Ptak-error estimates,
{\it Appl.\ Math.\ and Computation}, {\bf 62}, 1 (1994), 1--15; Math.\ Rev.\
95c:65087, Mihai Turinici.
\item[150.] A convergence theorem for Newton-like methods under generalized
Chen-Yamamoto-type assumptions, {\it Appl.\ Math.\ and Comput.}, {\bf 61}, 1
(1994), 25--37; Math.\ Rev.\ 65g:65082.
\item[151.] On the convergence of some projection methods and inexact
Newton-like iterations, {\it Tamkang J.\ Math.}, Vol.\ 25, No.\ 4 (1994),
335--341; Math.\ Rev.\ 95m:65105, Mihai Turinici.
\item[152.] On Newton's method and nonlinear operator equations, {\it P.U.J.M.},
Vol.\ 27 (1994), 34--44; Math.\ Rev.\ Author index 1996.
\item[153.] On the midpoint iterative method for solving nonlinear operator
equations and applications to the solution of integral equations, {\it Revue
D'analyse Numerique et de Theorie de l'approximation}, Tome 23, fasc.\ 2 (1994),
139--152; Math.\ Rev.\ 97j:65093.
\item[154.] Parameter based algorithms for approximating local solutions of
nonlinear complex equations, {\it Proyecciones}, Vol.\ 13, No.\ 1 (1994),
53--61; Math.\ Rev.\ 95f:65100.
\item[155.] The Halley-Werner method in Banach spaces, {\it Revue D'analyse
Numerique et de Theorie de l'approximation}, Tome 23, fasc.\ 2 (1994), 1--14;
Math.\ Rev.\ 96c:65099, G.\ Alefeld (CD-KLRH-A; Karlsruhe).
\item[156.] On a multistep Newton method in Banach spaces and the Ptak error
estimates, Proceeding of the Tenth Annual Conference on Applied Mathematics, CAM 94,
University of Central Oklahoma, Edmond (1994), 1--15.
\item[157.] Error bound representations of Chebysheff-Halley-type methods in
Banach spaces, {\it Rev.\ Aca\-demia de Ciencias Zaragoza}, {\bf 49} (1994),
57--69; Math.\ Rev.\ 95j:65065.
\item[158.] On the monotone convergence of fast iterative methods in partially
ordered topological spaces, Proceedings of the Tenth Annual Conference on Applied
Mathematics, CAM 94, University of Central Oklahoma, Edmond (1994), 16--19.
\item[159.] On the discretization of Newton-like methods, {\it Internat.\ J.\
Computer.\ Math.}, Vol.\ 52 (1994), 161--170.
\item[160.] A local convergence theorem for the super-Halley method in a
Banach space, {\it Appl.\ Math.\ Lett.}, Vol.\ 7, No.\ 5 (1994), 49--52; Math.\
Rev.\ Author index 1996.
\item[161.] A convergence analysis for a rational method with a parameter in
Banach space, {\it Pure Mathematics and Applications}, {\bf 5}, 1 (1994),
59--73; Math.\ Rev.\ 95j:65063.
\item[162.] On sufficient conditions of the convergence and an optimality of
error estimate for a high speed iterative algorithm for solving nonlinear
algebraic systems, {\it Chinese J.\ Math.}, Vol.\ 22, No.\ 4 (1994), 373--384;
Math.\ Rev.\ 95i:65078, Xiaojun Chen.
\item[163.] On the convergence of modified contractions, {\it Journ.\ Comput.\
Appl.\ Math.}, {\bf 55}, 2 (1994), 183--189; Math.\ Rev.\ 96a:65085.
\item[164.] A multipoint Jarratt-Newton-type approximation algorithm for
solving nonlinear operator equations in Banach spaces, {\it Functiones et
Aproximatio Commentarii Matematiki}, {\bf XXIII} (1994), 97--108; Math.\ Rev.\
96c:65098.
\item[165.] Convergence results for the super-Halley method using divided
differences, {\it Functiones et Approximatio Commentari Mathematici}, {\bf XXIII}
(1994), 109--122; Math.\ Rev.\ 96d:6509.
\item[166.] On the aposteriori error estimates for Stirling's method, {\it
Studia Scientiarum Mathematicarum Hungarica}, {\bf 30}, 3--4 (1995), 205--216;
Math.\ Rev.\ 96g:65055, Otmar Scherzer (1-DE; Newark, DE).
\item[167.] Sufficient conditions for the convergence of Newton-like methods under
weak smoothness assumptions, {\it Mathematics}, CAM 95, Edmond, OK (1995), Proceedings
of the Eleventh Conference on Computational and Applied Mathematics (1995),
1--13.
\item[168.] On Stirlin's method, {\it Tamkang J.\ Math.}, Vol.\ 27, No.\ 1 (1995).
\item[169.] Stirling's method and fixed points of nonlinear operator equations in
Banach space, {\it Bulletin of the Institute of Mathematics Academic Sinica},
Vol.\ 23, No.\ 1 (1995), 13--20; Math.\ Rev.\ 96b:65060, A.M.\ Galperin (IL-BGUN;
Be'er Sheva).
\item[170.] Error bounds for fast two-point Newton methods of order four,
{\it Mathematics}, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh
Annual Conference on Computational and Applied Mathematics (1995), 14--18.
\item[171.] Improved error bounds for fast two-point Newton methods of order
three, {\it Mathematics}, CAM 95, Edmond, OK (1995), Proceedings of the
Eleventh Annual Conference on Computational and Applied Mathematics (1995),
19--23; {\it Rev.\ Academia de Ciencias, Zaragoza}, {\bf 50} (1995), 15--19;
Math.\ Rev.\ Author index 1996.
\item[172.] Stirling's method in generalized Banach spaces, {\it Annales Univ.\
Sci.\ Budapest.\ Sect.\ Comp.}, {\bf 15} (1995), 37--47; Math.\ Rev.\
97m:47093 (George Isac).
\item[173.] A unified approach for constructing fast two-step Newton-like
methods, {\it Monatshefte fur Mathematik}, {\bf 119} (1995), 1--22; Math.\ Rev.\
96a:65093, Otmar Scherzer (1-TXAM; College Station, TX).
\item[174.] On the Secant method and the Ptak error estimates, {\it Revue
d'analyse Numerique et de theorie de l'approximation}, {\bf 24}, 1--2 (1995),
3--14;  Math. Rev. 1998, pp. 58.
\item[175.] An error analysis for the secant method under generalized
Zabrejko-Nguen-type assumptions, {\it Arabian Journal of Science and Engineering},
{\bf 20}:1 (1995), 197--206; Math.\ Rev.\ 96c:65100, A.M.\ Galperin
(IL-BGUN; Be'er Sheva).
\item[176.] Optimal-order parameter identification in solving nonlinear
systems in a Banach space, {\it Journal of Computational Mathematics},
{\bf 13}, 3 (1995), 267--280; Math.\ Rev.\ 96j:65070, A.A.\ Fonarev (Moscow).
\item[177.] Nondifferentiable operator equations on Banach spaces with a
convergence structure, {\it Pure Mathematics and Applications}, ({\it PUMA}),
Vol.\ 6, 1 (1995), Math.\ Rev.\ 97h:47062.
\item[178.] Perturbed Newton-like methods and nondifferentiable operator
equations on Banach spaces with a convergence structure, ({\it SWJPAM}) {\it 
Southwest Journal of Pure and Applied Mathematics}, {\bf 1} (1995), 1--12;
Math.\ Rev.\ 97k:65139, A.M.\ Galperin.
\item[179.] Results on controlling the residuals of perturbed Newton-like
methods on Banach spaces with a convergence structure, ({\it SWJPAM})
{\it Southwest Journal of Pure and Applied Mathematics}, {\bf 1} (1995),
32--38; Math.\ Rev.\ 97k:65140.
\item[180.] A study on the order of convergence of a rational iteration for
solving quadratic equations in a Banach space, {\it Rev.\ Academia de Ciencias,
Zaragoza}, {\bf 50} (1995), 35--40; Math.\ Rev.\ Author index 1996.
\item[181.] On an application of a variant of the closed graph theorem to
the solution of nonlinear equations, {\it Pure Mathematics and Applications},
({\it PUMA}), {\bf 6}, 4 (1995), 301--312; Math.\ Rev.\ 97b:47063, M.Z.\
Nashed.
\item[182.] Results on Newton methods; Part I: A unified approach for
constructing perturbed Newton-like methods in Banach space and their applications,
{\it Appl.\ Math.\ and Comp.}, {\bf 74}, 2--3 (1996), 119--141; Math.\ Rev.\
97b:65074, De Ren Wang.
\item[183.] Results on Newton methods; Part II: Perturbed Newton-like methods
in generalized Banach spaces, {\it Appl.\ Math.\ and Comp.}, {\bf 74}, 2--3
(1996), Math.\ Rev.\ 97b:65075, De Ren Wang.
\item[184.] On the method of tangent hyperbolas, {\it Journal of Approximation
Theory and Its Applications}, {\bf 12}, 1 (1996), 78--96.
\item[185.] A unified approach for constructing fast two-step methods in Banach
space and their applications, Proc.\ 12th Conference CAM 96, Computational
and Applied Math., Edmond, OK, (1996), 1--50.
\item[186.] On the method of tangent parabolas, {\it Functiones et
Approximatio Commentarii Mathematici}, {\bf XXIV} (1996), 3--15; Math. Rev.
98a:65077.
\item[187.] On an extension of the mesh-independence principle for operator
equations in Banach space, {\it Appl.\ Math.\ Lett.}, Vol.\ 9, No.\ 3 (1996),
1--7; Math.\ Rev.\ 97a:47108.
\item[188.] An inverse-free Jarratt type approximation in a Banach space,
{\it Journal of Approximation Theory and Its Applications}, {\bf 12}, 1 (1996),
19--30; Math Rev. 1998, pp. 58.
\item[189.] An error analysis for the Steffensen method under generalized
Zabrejko-Nguen-type assumptions, {\it Revue d'analyse Numerique et de theorie de
l'approximation}, {\bf 25}, 1--2 (1996), 11--22.
\item[190.] Concerning the convergence of inexact Newton-like methods on
Banach spaces with a convergence structure and applications, Proceedings of the
International Conference on Approximation and Optimization (Romania) - ICAOR
Cluj-Napoca, July 19--August 1,  (1996), 163--172; Math. Rev. 98j:65040.
\item[191.] Improved error bounds for an Euler-Chebysheff-type method,
{\it Pure Math.\ Appl.} ({\it PUMA}), {\bf 7}, 1--2 (1996), 41--51; Math.\
Rev.\ 97j:65097.
\item[192.] On the convergence of perturbed Newton-like methods in Banach
space and applications, {\it Southwest J.\ Pure Appl.\ Math.}, {\bf 2} (1996),
34--41; Math Rev. 98b:65060.
\item[193.] Sufficient conditions for the convergence of iterations to points
of attraction in Banach spaces, {\it Southwest J.\ Pure Appl.\ Math.}, {\bf 2}
(1996), 42--47; Math. Rev. 98b:65061.
\item[194.] Weak conditions for the convergence of iterations to solutions
of equations on partially ordered topological spaces, {\it Southwest J.\ Pure
Appl.\ Math.}, {\bf 2} (1996), 48--54; Math Rev. 98b:65062.
\item[195.] On the monotone convergence of implicit Newton-like methods,
{\it Southwest J.\ Pure Appl.\ Math.}, {\bf 2} (1996), 55--59; Math
Rev. 98b:65063.
\item[196.] A generalization of Edelstein's theorem on fixed points and applications,
{\it Southwest J.\ Pure Appl.\ Math.}, {\bf 2} (1996), 60--64; Math. Rev.
98a:65078.
\item[197.] Generalized conditions for the convergence of inexact Newton
methods on Banach spaces with a convergence structure and applications,
{\it Pure Mathematics and Applications} ({\it PUMA}), {\bf 7}, 3--4 (1996),
197--214; Math.\ Rev.\ Author index 1997.
\item[198.] Error bounds for an almost fourth order method under generalized
conditions, {\it Rev.\ Academia de Ciencias, Zaragoza}, {\bf 51} (1996),
19--26; Math. Rev. 98c:65091, Tetsuro Yamamoto.
\item[199.] A simplified proof concerning the convergence and error bound
for a rational cubic method in Banach spaces and applications to nonlinear
integral equations, {\it Rev.\ Academia de Ciercias, Zaragoza}, {\bf 51}
(1996), 47--55; Math.\ Rev. 98e:65074, Xiaojun Chen.
\item[200.] On the convergence of Chebysheff-Halley-type method using
divided differences of order one, {\it Rev.\ Academia de Ciercias, Zaragoza},
{\bf 51} (1996), 27--45; Math. Rev. 98d:65074..
\item[201.] On the convergence of two-step methods generated by point-to-point
operators, {\it Appl.\ Math.\ and Comput.}, {\bf 82}, 1 (1997), 85--96;
Math.\ Rev.\ 97m:65107, A.M.\ Galperin, Boro D\"oring.
\item[202.] Improved error bounds for Newton-like iterations under
Chen-Yamamoto assumptions, {\it Appl.\ Math.\ Lett.}, {\bf 10}, 4 (1997),
97--100; Math.\ Rev.\ 1998, pp. 59.
\item[203.] Inexact Newton methods and nondifferentiable operator equations on
Banach spaces with a convergence structure, {\it Approx.\ Th.\ Applic.},
{\bf 13}, 3 (1997), 91--104.
\item[204.] A mesh independence principle for inexact Newton-like methods and
their discretizations under generalized Lipschitz conditions, {\it Appl.\ Math.\
Comp.}, {\bf 87} (1997), 15--48; Math.\ Rev.\ 98d:65075, Asen L.\ Dontchev.
\item[205.] On the super-Halley method using divided differences, {\it Appl.\
Math.\ Lett.}, {\bf 10}, 4 (1997), 91--95; Math.\ Rev.\ 1998, pp. 59.
\item[206.] Chebysheff-Halley like methods in Banach spaces, {\it Korean Journ.\ 
Comp.\ Appl.\ Math.}, Vol.\ 4, No.\ 1 (1997), 83--107; Math.\ Rev.\ 98a:47068,
Tetsuro Yamamoto.
\item[207.] Concerning the convergence of inexact Newton methods, {\it J.\
Comp.\ Appl.\ Math.}, {\bf 79} (1997), 235--247; Math.\ Rev.\ 98c:
47077, P.P.\ Zabrejko.
\item[208.] General ways of constructing accelerating Newton-like iterations
on partially ordered topological spaces, {\it Southwest Journal of Pure and
Applied Mathematics}, {\bf 1} (1997), 18--22.
\item[209.] Smoothness and perturbed Newton-like methods, {\it Pure Mathematics
and Applications} ({\it PUMA}), {\bf 8}, 1 (1997), 13--28; Math.\ Rev.\
98h:65023.
\item[210.] A mesh independence principle for operator equations and
Steffensen-method, {\it Korean J.\ Comp.\ Appl.\ Math.}, {\bf 4}, 2 (1997),
263--280; Math.\ Rev.\ 98c:65092.
\item[211.] Improving the rate of convergence of Newton methods on Banach spaces
with a convergence structure and applications, {\it Appl.\ Math.\ Lett.}, {\bf 10},
6 (1997), 21--28; Math.\ Rev.\ 1999, pp. 59.
\item[212.] A new convergence theorem for Steffensen's method on Banach spaces
and applications, {\it Southwest Journal of Pure and Applied Mathematics},
{\bf 1} (1997), 23--29.
\item[213.] A local convergence theorem for the inexact Newton method at singular
points, {\it Southwest Journal of Pure and Applied Mathematics}, {\bf 1} (1997),
30--36.
\item[214.] Applications of a special representation of analytic functions,
{\it Southwest Journal of Pure and Applied Mathematics}, {\bf 2} (December 1997),
43--47.
\item[215.] On a new Newton-Mysovskii-type theorem with applications to inexact
Newton-like methods and their discretizations, {\it IMA J.\ Num.\ Anal., Journal
of the Institute of Mathematics and Its Applications}, {\bf 18} (1997),
37--56.
\item[216.] Results involving nondifferentiable equations on Banach spaces
with a convergence structure and Newton methods,
{\it Rev.\ Academia de Ciencias, de Zarayoza}, {\bf 52} (1997), 23--30.
\item[217.] The asymptotic mesh independence principle for inexact
Newton-Galerkin-like methods, {\it PUMA}, {\bf 8}, 2-3-4, (1997), 169--194.
\item[218.] The Halley method in Banach spaces and the Ptak error estimates,
{\it Rev.\ Academia de Ciencias, de Zaragoza}, {\bf 52} (1997), 31--41.
\item[219.] Comparing the radii of some balls appearing in connection to three local
convergence theorems for Newton's method, {\it Southwest J.\ Pure Appl.\ Math.},
{\bf 1} (1998), 24--28.
\item[220.] On the monotone convergence of an Euler-Chebysheff-type method in
partially ordered topological spaces, {\it Revue d'analyse Numerique et de theorie
de l'approximation}, {\bf 27}, 1 (1998), 23--31.
\item[221.] Sufficient conditions for constructing methods faster than Newton's,
{\it Appl.\ Math.\ Comp}, {\bf 93} (1998), 169--181.
\item[222.] Error bounds for the Chebyshev method in Banach spaces,
{\it Bull.\ Inst.\ Acad.\ Sinica}, {\bf 26}, 4 (1998), 269--282.
\item[223.] Improving the rate of convergence of some Newton-like methods for the
solution of nonlinear equations containing a nondifferentiable term, {\it
Revue d'analyse Numerique et de theorie de l'approximation}, {\bf 27}, 2 (1998),
191--202.
\item[224.] On the convergence of a certain class of iterative procedures
under relaxed conditions with applications, {\it J. Comp.\ Appl.\ Math.},
{\bf 94} (1998), 13--21.
\item[225.] Improving the order and rates of convergence for the
Super-Halley method in Banach spaces, {\it Korean J.\ Comp.\ Appl.\ Math.},
{\bf 5}, 2 (1998), 465--474.
\item[226.] A new convergence theorem for the Jarratt method in Banach spaces, 
{\it Computers and Mathematics with Applications}, {\bf 36}, 8 (1998),
13--18.
\item[227.] On Newton's method under mild differentiability conditions and
applications, {\it Appl.\ Math.\ Comp.}, {\bf 102} (1999), 177--183.
\item[228.] Improved error bounds for a Chebysheff-Halley-type method,
{\it Acta Math. Hungarica}, {\bf 84}, (3) (1999), 209--219.
\item[229.] Convergence rates for inexact Newton-like methods at singular
points and applications, {\it Appl. Math. Comp.}, {\bf 102} (1999), 185--201.

\item[230.] Convergence domains for some iterative processes in Banach
spaces using outer and generalized inverses, {\it J. Computational
Analysis and Applications}, Vol. 1, No. 1, (1999), 87--104.
\item[231.] Concerning the convergence of a modified Newton-like method,
{\it Zeitschrift f\"ur analysis und ihre Anwendungen, Journal for Analysis
and Applications}, {\bf 18}, (3) (1999), 785--792.
\item[232.] A new convergence theorem for Newton-like methods in Banach
space and applications, {\it Comput.\ Appl.\ Math.}, {\bf 18}, 3 (1999).

\item[233.] A new convergence theorem for inexact Newton methods based on
assumptions involving the second Fr\'echet-derivative,
{\it Computers and Mathematics with Applications}, {\bf 37} (1999), 109--115.
\item[234.] The Halley-Werner method in Banach spaces and the Ptak error estimates,
{\it Bulletin Hong-Kong Math. Soc. BHKMS}, Vol. 2 (1999), 357--371.
\item[235.] Concerning the radius of convergence of Newton's method and applications,
{\it Korean J. Comp. Appl. Math.}, Vol. 6, No. 3 (1999), 451--462.
\item[236.] Relations between forcing sequences and inexact-Newton-like
iterates in Banach space, {\it Intern. J. Comp. Math.}, {\bf 71} (1999),
235--246.
\item[237.] On the applicability of two Newton methods for solving equations
in Banach space, {\it Korean J. Comp. Appl. Math.}, Vol. 6, No. 2 (1999),
267--275.
\item[238.] Affine invariant local convergence theorems for inexact
Newton-like methods, {\it Korean J. Comp. Appl. Math.}, Vol. 6, No. 2 (1999),
291--304.
\item[239.] A convergence analysis for Newton-like methods in Banach space
under weak hypotheses and applications, {\it Tamkang J. Math.}, Vol. 30, No.
4 (1999), 253--261.
\item[240.] An error analysis for the midpoint method, {\it
Tamkang J. Math.}, Vol. 30, No. 2 (1999), 71--83.
\item[241.] Appproximating solutions of operator equations using modified
contractions and applications, {\it Studia Scientiarum Mathematicurum Hungarica},
\item[242.] Convergence results for a fast iterative method in linear spaces,
{\it Taiwanese J. Math.} {\bf 3}, 3 (1999), 323--338.
\item[243.] A generalization of Ostrowski's theorem on fixed points,
{\it Appl. Math. Letters}, {\bf 12} (1999), 77--79.
\item[244.] A new Kantorovich-type theorem for Newton's method,
{\it Applicationes Mathematicae} {\bf 26}, 2 (1999), 151--157.
\item[245.] A monotone convergence theorem for Newton-like methods using
divided differences of order two, {\it Southwest J. Pure Appl. Math.}
{\bf 1} (1999).
\item[246.] On the convergence of Newton's method for polynomial
equations and applications in radiative transfer, {\it Monatschefte f\"ur
Mathematik}, {\bf 27} (1999), 265--276.
\item[247.] On the convergence of Steffensen-Aitken-like methods using
divided differences obtained recursively, {\it Rev. Anal. Numer. Theor.
Approx.} {\bf 28}, 2 (1999), 109--117.
\item[248.] Local and global convergence results for a class of 
Steffensen-Aitken-type methods, {\it Adv. Nonlinear Var. Ineq.} {\bf 2},
2 (1999), 117--126.
\item[249.] Relations between forcing sequences and inexact Newton iterates
in Banach space, {\it Computing}, {\bf 63} (1999), 131--144.
\item[250.] A new convergence theorem for the method of tangent
hyperbolas in Banach space, {\it Projecciones}, {\bf 18}, 1 (1999), 1--11.
\item[251.] Local convergence of inexact Newton methods under affine
invariant conditions and hypotheses on the second Fr\'echet-derivative,
{\it Applicationes Mathematicae}, {\bf 26}, 4 (1999), 457--465.
\item[252.] Newton methods on Banach spaces with a convergence structure and
applications, {\it Computers and Math.\ with Appl.\ Intern.\ J.}, Pergamon Press,
(2000).
\item[253.] Accessibility of solutions of equations on Banach spaces by
Newton-like methods and applications, {\it Bulletin Inst. Math. Acad.
Sinica}, Vol. 28, No. 1 (2000).
\item[254.] Forcing sequences and inexact Newton iterates in Banach space,
{\it Appl. Math. Letters}, {\bf 13} (2000), 77--80.
\item[255.] Choosing the forcing sequences for inexact Newton methods in
Banach space, {\it Comput. Appl. Math.}, {\bf 19}, 1 (2000).
\item[256.] Conditions for the convergence of perturbed Steffensen
methods on a Banach space with a convergence structure, {\it Adv. Nonlinear
Var. Inequal}, {\bf 3}, 1 (2000), 23--35.
\item[257.] On some general iterative methods for solving nonlinear
operator equations containing a nondifferentiable term, {\it Adv. Nonlinear
Var. Inequal.}, {\bf 3}, 1 (2000), 15--21.
\item[258.] A mesh independence principle for perturbed Newton-like
methods and their discretizations, {\it Korean J. Comp. Appl. Math.}, {\bf 7},
1 (2000), 139--159.
\item[259.] A convergence theorem for Newton-like methods in Banach
space under general weak assumptions and applications, {\it Communications
on Applied Analysis}, {\bf 7}, 2 (2000), 57--72.
\item[260.] Error bounds for the Halley-Werner method in Banach spaces,
{\it Communications on Applied Nonlinear Analysis}, {\bf 7}, 2 (2000),
73--85.
\item[261.] Extending the region of convergence for a certain class of modified
iterative methods on Banach space and applications,
{\it Adv. Nonlinear Var. Inequalities}, {\bf 3}, 1 (2000), 1--5.
\item[262.] Improved error bounds for Newton's method under hypotheses
on the second Fr\'echet-derivative, {\it Adv. Nonlinear Var. Inequal.},
{\bf 3}, 1 (2000), 37--45.
\item[263.] Local convergence of inexact Newton-like iterative methods and applications,
{\it Computers and Mathematics with Applications}, {\bf 39} (2000),
69--75..
\item[264.] A unifying semilocal convergence theorem for Newton-like methods in
Banach space, {\it Pan American Mathematical Journal}, {\bf 10}, 1 (2000),
95--99.
\item[265.] Perturbed Steffensen-Aitken projection methods for solving
equations with nondifferentiable operators, {\it PUNJAB J. Math.}, {\bf XXXII}
(2000).
\item[266.] Semilocal convergence theorems for a certain class
of iterative procedures using outer or generalized inverses, {\it Korean J.
Comp. Appl. Math.}, {\bf 7} 1 (2000), 29--40.
\item[267.] A new semilocal convergence theorem for Newton's method in Banach space
using hypotheses on the second Fr\'echet-derivative,
{\it Journal of Comput. Appl. Math.} (2000).
\item[268.] Improving the order of convergence of Newton's method
for a certain class of polynomial equations, {\it SooChow J. Math.},
{\bf 26}, 2 (2000), 117--122.
\item[269.] 
 A fixed point proof of the convergence of extended Newton-like
methods on Banach spaces and applications, {\it Commun.\ Appl.\ Anal}.
\item[270.] A new fixed point theorem for perturbed Newton-like methods on Banach
space and applications to the solution of nonlinear integral equations appearing
in radiative transfer, {\it Commun.\ Appl.\ Anal}.
\item[271.] On the convergence of Steffensen-Galerkin methods, {\it 
Atti del seminario Matematica e Fisico dell'universita di Modena}.
\item[272.] Generalized conditions for the convergence of inexact Newton-like
methods on Banach spaces with a convergence structure and applications,
{\it Korean J.\ Comp.\ Appl.\ Math}.

\item[273.] A convergence theorem for Newton's method under uniform-like
continuity conditions on the second Fr\'echet-derivative, {\it
Atti del seminario Matematica e Fisico dell' universita di Mondena},
{\bf XLVIII} (2000), 235--243.
\item[274.] A new convergence theorem for Stirling's method in Banach
space, {\it Atti del seminario Matematica e Fisico dell'
universita di Modena}, {\bf XLVIII} (2000), 225--233.

\item[275.] Inexact  Steffensen-Aitken  methods for solving equations,
{\it Pan American Mathematical Journal}.
\item[276.]  Steffen-Aitken-type methods and 
 implicit functions, {\it Pan American Mathematical Journal}.
\item[277.] On controlling the residuals of some iterative
methods, {\it Communications on Applied Nonlinear Analysis}.
\item[278.] The Steffenson method on special Banach spaces, {\it
Communications on Applied Nonlinear Analysis}.
\item[279.] A new convergence theorem for the Steffenson method in
Banach space and applications, {\it Mathematica-Revue}.
\item[280.] The Chebyshev method in Banach spaces and the Ptak error estimates,
{\it Advances in Nonlinear Variational Inequalities}.
\item[281.] An error analysis for Steffensen's method, {\it Pan American
Mathematical Journal}.
\item[282.] A convergence theorem for Steffensen's method and the Ptak error
estimates, {\it Advances in Nonlinear Variational Inequalities}.
\item[283.] Iterative methods 
 of order between 1.618$\ldots$ and 1.839$\ldots$, {\it
Communications on Applied Nonlinear Analysis}.
\item[284.] Convergence theorems for Newton-like methods under generalized
Newton-Kantorovich conditions, {\it Advances in Nonlinear
Variational Inequalities}.
\item[285.] On the local convergence of m-step Newton methods with applications
on a vector supercomputer, {\it Advances in Nonlinear Variational
Inequalities}.
\item[286.] Concerning the monotone convergence of the method
of tangent hyperbolas, {\it Korean J. Comp. Appl. Math.}
\item[287.] Perturbed Newton  methods in generalized Banach spaces,
{\it Commun. Appl. Math}.
\item[288.]  On the convergence of an Euler-Chebysheff-type method using divided
differences of order one, {\it Communications on Applied Nonlinear
Analysis}.
\item[289.] On the convergence of disturbed Newton-like methods in Banach space,
{\it Pan American Mathematical Journal}.

\item[290.] Error bounds for the Halley method in Banach spaces,
{\it Advances in Nonlinear Variational Inequalities}.
\item[291.]  Error bounds for the midpoint method in Banach spaces,
{\it Communications on Applied Nonlinear Analysis}.
\item[292.] Enlarging the region of convergence for 
a certain iterative method, {\it Pan American Mathematical Journal}.
\item[293.] A new convergence theorem for the method of tangent
parabolas in Banach space, {\it Pan American Mathematical Journal}.
\item[294.] Improving the rate of convergence of Newton-like methods in Banach
space using twice Fr\'echet-differentiable operators and applications,
{\it Pan American Mathematical Journal}.
\item[295.] On the solution of nonlinear equations under Holder continuity
assumptions, {\it Commun. Appl. Anal.} 
\item[296.] On the convergence of a Newton-like method based on
$m$-Fr\'echet differentiable operators and applications in radiative
transfer, {\it Journal of Computational Analysis and Applications}.
\item[297.] On the radius of convergence of Newton-like methods,
{\it Communications in Applied Analysis}.
\item[298.] Convergence domains for some iterative procedures in Banach
spaces, {\it Communications in Applied Analysis}.
\item[299.] Error bounds for Newton's method under hypotheses on the
$m$th Fr\'echet-derivative, {\it Advances in Nonlinear Variational
Inequalities}.
\item[300.] Local convergence theorems for Newton methods, {\it Korean J.
Comp. Appl. Math.}.
\item[301.] The effect of rounding errors on a certain class of iterative
methods, {\it Applicationes Mathematicae}.
\item[302.] On the local convergence of $m$-step Newton methods and
$J$-Fr\'echet differentiable operators with applications on a vector
super computer, {\it Communications on Applied Nonlinear Analysis}.
\item[303.] Semilocal convergence theorems for Newton's method using
outer inverses and hypotheses on the $m$th Fr\'echet-derivative,
{\it Mathematical Sciences Research}.
\item[304.] A modification of the Newton-Kantorovich hypotheses for
the convergence of Newton's method, {\it Advances in Nonlinear Variational
Inequalities}.
\item[305.] Convergence results for Newton's method involving smooth
operators, {\it Mathematical Sciences Research}.
\item[306.] The effect of rounding errors on Newton methods,
{\it Korean J. Comp. Appl. Math}.
\item[307.] Local convergence theorems of Newton's method 
for nonlinear equations using outer or generalized inverses,
{\it Chechoslovak Math. J.}
\item[308.] Convergence reuslts for nonlinear equations
under generalized H\"older continuity assumptions, {\it Communications
in Applied Nonlinear Analysis}.
\end{enumerate}

%%%%%
\begin{center}
{\bf Submitted for Publication}
\end{center}

\begin{enumerate}
\item[309.] On the monotone convergence of a Chebysheff-Halley-type method in
partially ordered topological spaces.
\item[310.] Semilocal convergence results for Newton-like methods using
Kantorovich quasi-majorant functions involving the first derivative.
\item[311.] A new convergence theorem for the secant method in Banach space
and applications.
\item[312.] Convergence theorems for some variants of Newton's method
of order greater than two.
\item[313.] Accessibility of solutions of equations on Banach spaces by a
Stirling-like method.
\item[314.] A Newton-Kantorovich theorem for equations involving 
$m$-Fr\'echet differentiable operators and applications in radiative transfer.
\item[315.] On the radius of convergence of Newton's method.
\item[316.] On a new method for enlarging the radius of convergence
for Newton's method.
\item[317.] A semilocal convergence theorem for inexact Newton methods
involving $m$-Fr\'echet derivatives.
\item[318.] Relations between forcing sequences and inexact Newton iterates
involving $m$-Fr\'echet-differentiable operators.
\item[319.] Forcing sequences and inexact iterates involving
$m$-Fr\'echet differentiable operators.
\item[320.] Local convergence of iterative methods under affine
invariant conditions and hypotheses on the $m$th Fr\'echet-derivative.
\item[321.] Local convergence of a certain class of iterative
methods and applications.
\item[322.] A new semilocal convergence theorem for Newton's
method using hypotheses on the $m$-Fr\'echet derivative.
\end{enumerate}



\begin{center}
{\bf Under Preparation}
\end{center}
\begin{enumerate}
\item[323.] Choosing the forcing sequences for inexact
Newton methods and $m$-Fr\'echet differentiable operators.
\item[324.] Semilocal convergence theorems for a certain class
of iterative procedures involving $m$-Fr\'echet differentiable operators.
\item[325.] Local convergence theorems for Newton's method using outer
or generalized inverses and $m$-Fr\'echet differentiable operators.
\item[326.] Relaxing convergence conditions for Newton-like methods.
\item[327.] Convergence domains of Newton-like methods for solving equations
under weakened assumptions.
\item[328.] 
 Semilocal convergence theorems for Newton's method using outer
inverses and hypotheses on the second Fr\'echet-derivative.
\end{enumerate}

\medskip
\noindent
(J) {\bf Other}

\medskip
The following professors have requested papers:

\begin{enumerate}
\item[1.] Etzio Venturino, University of Iowa, (Dept.\ Math.), USA
\item[2.] A.G.\ Kartsatos, University of South Florida, (Dept.\ Math.),
USA
\item[3.] H.\ Jarchow, Institute fur Angewandte Mathematik der 
Universitat Zurich Ch-8001 Zurich, Switzerland.
\item[4.] M.S.\ Khan, King Abdulaziz University, (Dept.\ Math.), Saudi
Arabia
\item[5.] Manfred Knebusch, Universitat Regensburg Fakultat fur Mathematik
8400 Regensburg Universitatsstrabe 31, West Germany
\item[6.] Ernest J.\ Eckert, College of Environmental Sciences, The University of
Wisconsin-Green Bay, 2420 Nicolet Dr., Green Bay, WI 54302, USA
\item[7.] Josef Danes, Mathematical Institute Charles University, Sokolovska
83 18600 Prague 8-Karlin, Chechoslovakia
\item[8.] Goral Reddy, Dept.\  of Mathematics, St.\ Andrews, Scotland
\item[9.] Jerzy Popenda, Dept.\ of Math., Univesity of Poznan, Poland
\item[10.] Vlastimil Ptak, Chechoslovak Academy of Science, Praha,
Chechoslovakia
\item[11.] Alejandro Figueroa, Universidad de Magallanes, Punta
Arenas-Chile
\item[12.] Dragan Jucic, Osijek, Yugoslavia
\item[13.] Ahmad B.\ Casdam, Multan, Pakistan
\item[14.] Luis Saste Habana, Cuba
\item[15.] S.N.\ Mishra, Lesotho, Africa
\item[16.] Josef Kral, Prague, Checholovakia
\item[17.] Juan J.\ Nieto, Santiago, Spain
\item[18.] S.D.\ Chatterji, Lausanne, Switzerland
\item[19.] Peter Madhe, Berlin, Germany
\item[20.] Ioan Muntean, Cluj, Romania
\item[21.] S.L.\ Singh, Xardwar, India
\item[22.] P.D.N.\ Sriniras, India
\item[23.] S.\ Grzegorskii, Lublin, Poland
\item[24.] Toma's Arechaga, Aires, Argentina
\item[25.] J.D.\ Deader, Salt Lake, Utah, USA
\item[26.] P.\ Drouet, Rhone, France
\item[27.] J.\ Weber, The University of Wisconsin, Milwakee, WI, USA
\item[28.] David C.\ Kurtz, Rollins College, USA
\item[29.] Jorge L.\ Quiroz, Colima, Mexico
\item[30.] Ming-Po Chen, Taiwan, Republic of China
\item[31.] Mustafa Telci, Begtepe, Ankara, Turkey
\item[32.] Helmut Dietrich, Merseburg, Germany
\item[33.] Dong Chen, Fayeteville, Arkansas, USA
\item[34.] Mohammad Tabatabai, Cameron University, OK, USA
\item[35.] M.S.\ Khan, Sultan Quboos University, Muscat, Saltanate of Oman
\item[36.] Laszlo Mate, Technical University, Budapest, Hungary
\item[37.] H.K.\ Pathak, Bhilai Nayar, India
\item[38.] Osvaldo, Pino Garcia, Havana, Cuba
\item[39.] B.K.\ Sharma, Ravishankar University, Raipur, India
\item[40.] Aied Al-Knazi, King Abdul Aziz Univ., Jeddah, Saudi Arabia
\item[41.] Hassan-Qasin, King Abdul Aziz Univ., Jeddah, Saudi Arabia
\item[42.] Tadeusz Jankowski, University Gdansk, Gdansk, Poland
\item[43.] K.\ Kurzak, University Teachers College, Dept.\ Chemistry,
Siedlce, Poland
\item[44.] R.\ Gonzalez, 2000 Rosario, Argentina
\item[45.] Emad Fatemi, Ecole Polytechnique Federale de Lausanne,
Switzerland
\item[46.] Prasad Balusu, University of Rochester, MI, USA
\item[47.] Dieter Schott, Rostolki, Germany
\item[48.] J.M.\ Martinez, IMECC-UNICAMP, Brazil
\item[49.] Prasad Balusu, India
\item[50.] Qun-sheng Zhou, P.R.\ China
\item[51.] W.\ Kliesch, Universitat Leipzig, Germany
\item[52.] Adriana Kindybalyuk, Ukraine Academy of Sciences, Kiev, Ukraine
\item[53.] Roman Brovsek, Ljubljana Slovenia
\item[54.] D.\ Mathieu, L.M.R.E., France
\item[55.] Donald Schaffner, Rutgers University, NJ, USA
\item[56.] David Ward, Barron Associates, Charlottesville, VA, USA
\item[57.] Eugene Parker, Barron Associates, Charlottesville, VA, USA
\item[58.] Miguel Gomez, Havana, Cuba
\item[59.] L.\ Brueggemann, Leipzig-Halle, Germany
\item[60.] Fidel Delgado, Havana, Cuba
\item[61.] B.C.\ Dhage, Maharashtra, India
\item[62.] Leida Perea, Havana, Cuba
\item[63.] David Ruch, Sam Houston University, Huntsville, Texas
\item[64.] Patrick J.\ Van Fleet, Sam Houston University, Huntsville, Texas
\item[65.] Tomas Arechaga, BS.\  Aires, Argentina
\item[66.] M.A.\ Hernandez, Spain
\item[67.] J.\ Illuateau, Romania
\item[68.] Ioan A.\ Rus, University of Cluj-Napoca, Romania
\item[69.] V.K.\ Jain, Kharagpur, India
\item[70.] Alan Lun, University of Melbourne, Victoria, Australia
\item[71.] A.M.\ Saddeek, Assiut University of Mathematics, Assiut,
A.R.\ Egypt
\item[72.] Miguel A.\ Hernandez, Dept.\ of Mathematics, University de la
Rioja, Loyrono, Spain
\item[73.] James L.\ Moseley, Dept.\ of Mathematics, West Virgina University,
Morgantown, WV 26500, USA
\item[74.] Onesimo Hernandez-Lema, CINVESTAV-IPN, Dept.\ of Mathematics, 
D.F.\ Mexico
\item[75.] R.L.V.\ Gonzalez, Rosario, Argentina
\item[76.] Jose A.\ Ezquerro, Logrono, Spain
\item[77.] N.\ Ramanujam, Bharathidasan University, Tamil Nadu, India
\item[78.] Drouet Pierre, Solaize, France
\item[79.] Michael Goldberg, Las Vegas, NV, USA
\item[80.] Pierre Drouet, Brignai, France
\item[81.] Ravishannar, Shukla, Raipur, India
\item[82.] W.\ Quapp, Leipzig, Germany
\item[83.] Emil Catinas, Cluj-Napoca, Romania
\item[84.] Ion Pavaloiu, Cluj-Napoca, Romania
\item[85.] Th.\ Schauze, Lahn, Germany
\item[86.] Ioan Lazar, Cluj-Napoca, Romania
\item[87.] Ch.\ Grossman, Dresden, Germany
\item[88.] Livinus, Uko, Medellin, Colombia
\item[89.] Z. Athanassov, Bulgarian Academy of Sciences, Sofia, Bulgaria
\item[90.] Zhenyu Huang, Nanjing P.R.\ China
\item[91.] John Neuberger, Northern Arizona University, Flagstaff, AZ, USA
\end{enumerate}

\medskip
\noindent
(K) {\bf Seminars}

\medskip
At the University of Iowa I game eight seminars per academic year.
I continue doing so at New Mexico State and Cameron University. During
my talks I  explain my current work.

\bigskip
\noindent
(L) {\bf Papers Presented as an Invited Speaker}

\begin{enumerate}
\item[1.] University of Berkeley, International Summer Institute on Nonlinear
Functional Analysis and Applications (1983). Title: ``On a contraction theorem
and applications".
\item[2.] Los Alamos Laboratories (organizers), Conference on Invariant
Imbedding, Transport Theory, and Integral Equations, Eldorado Hotel, Santa Fe,
NM (1988). Title: ``On a class of nonlinear equations arising in neutron
transport".
\item[3.] Annual Meeting of the American Mathematical Society \#863, San
Francisco, California, June 16--19, 1991. Title: ``On the convergence of
algorithmic models" (Chairman of the Numerical Analysis Session (\#516),
7:00 p.m. -- 9:55 p.m., Thursday, Jan.\ 17, 1991).
\item[4.] Mathematical Association of America, Oklahoma--Arkansas Section,
Spring 1991. Title: ``Improved bounds for the zeros of polynomials".
\item[5.] Annual Meeting of the American Mathematical Society \#871, Baltimore,
Maryland, Jan.\ 8--11, 1992. Title: ``On the midpoint iterative method for
solving nonlinear operator equations in Banach spaces".
\item[6.] CAM 92, Edmond, OK, March 27, 1992, University of Central Oklahoma.
Title: ``On the secant method under weak assumptions".
\item[7.] CAM 93, Edmond, OK, February 5, 1993, University of Central Oklahoma.
Title: ``On a two-point Newton method in Banach spaces of order four and applications".
\item[8.] As in (7). Title: ``Sufficient convergence conditions for iterations
schemes modeled by point-to-set mappings".
\item[9.] As in (7). Title: ``On a two-point Newton method in Banach spaces
and the Ptak error estimates".
\item[10.] CAM 94, Edmond, IK, February 4, 1994, University of Central
Oklahoma. Title: ``On the monotone convergence of fast iterative methods in
partially ordered topological spaces".
\item[11.] CAM 94, Edmond, OK, February 4, 1994, University of Central
Oklahoma. Title: ``On a multistep Newton method in Banach spaces and the Ptak
error estimates".
\item[12.] 56th Annual Meeting of the Oklahoma--Arkansas Session of the
Mathematical Association of America, March 24, 1994. Title: ``On an inequality
from applied analysis", (Analysis section). It was held at the University of
Searcy, Searcy, Arkansas.
\item[13.] CAM 95, Edmond, OK, February 10, 1995, University of Central
Oklahoma. Title: ``A mesh independence principle for nonlinear equations in
Banach spaces and their discretizations".
\item[14.] 57th Annual Meeting of the Oklahoma--Arkansas Session of the
Mathematical Association of America, March 1995, Southwestern Oklahoma
State University, Weatherford, Oklahoma. Title: ``On the discretization
of Newton-like methods".
\item[15.] CAM 96, Edmond, OK, February 9, 1996, University of Central
Oklahoma. Title: ``A unified approach for constructing fast two-step methods
in Banach space and their applications".
\item[16.] 58th Annual Meeting of the Oklahoma--Arkansas Session of the
Mathematical Association of America, March 22--23, 1996, Westark Community
College, Fort Smith, Arkansas. Title: ``Regions containing solutions of nonlinear
equations".
\item[17.] Second European Congress of Mathematics, International Conference
on Approximation and Optimization (ICAOR), Cluj-Napoca, Romania, July 29--August
1, 1996. Title: ``On Newton's method".
\item[18.] Regional \#919 Meeting ``Approximation in Mathematics" of the
American Mathematical Society in Memphis, TN, University of Memphis, March
21--22, 1997. Title: ``Newton methods on Banach spaces with a convergence
structure and applications". A.M.S.\ Abstract \#919-65-93.
\item[19.] International Conference on Approximation and Optimization,
Cluj-Napoca, Romania, May 26--30, 1998. Title: ``Relations between forcing
sequences and inexact Newton iterates in Banach space".
\item[20.] Coloquium Seminars University of Memphis, March 12, 1999.
Title: ``Recent Developments in Discretization Studies".
\end{enumerate}

\medskip
\noindent
(M) {\bf Selected Lectures Presented}
\begin{enumerate}
\item[1.] University of Georgia, 1982--1984
\item[2.] University of Iowa, 1984--1986
\item[3.] State University of Iowa, 1985
\item[4.] Northern University of Viginia, 1986, 1988
\item[5.] New Mexico State University, 1986--1990
\item[6.] University of Ohio, 1986
\item[7.] University of Iowa, 1986, 1988
\item[8.] University of New York, 1986--1988
\item[9.] University of Texas at El Paso, 1987--1990
\item[10.] University of Arizona, I.E.D., 1989, 1990
\item[11.] Portland State University, 1990
\item[12.] Cameron University, 1990
\item[13.] University of Central Oklahoma, 1992, 1993, 1994, 1995, 1996
\item[14.] University of Cyprus, Nicosia Cyprus, 1993
\end{enumerate}

\medskip
\noindent
(N) {\bf Other Meetings Attended}

\begin{enumerate}
\item[1.] American Mathematical Society/Mathematical Association of
America Annual Meetings, Denver, Colorado, 1983, and Phoenix, Arizona, 1989
\item[2.] SIAM Mathematical Meetings, Des Moines, Iowa, 1995
\item[3.] International Conference on Theory and Applications of
Differential Equations, Ohio University, Athens, Ohio, 1988
\item[4.] Annual Research Conferences of the Bureau of the Census, Arlington,
Virginia, March 21--24, 1993 and 1995.
\end{enumerate}

\newpage %%%
\noindent
5. {\bf TEACHING EXPERIENCE}

\medskip
\noindent
(A) {\bf Courses Taught}

\smallskip
{\bf   Graduate}
\begin{enumerate}
\item[1.] Numerical Solutions of Ordinary Differential Equations, 
Partial Differential Equations, Integral Equations,
Integral Differential Equations
\item[2.] The Finite Difference and the Finite-Element Method for
Ordinary Differential Equations and Partial Differential Equations
\item[3.] Differential Equations 
\item[4.] Partial Differential Equations
\item[5.] Special Topics in Functional Analysis, Numerical Functional
Analysis, and Differential Equations
\item[6.] Numerical Solution of Functional Equations
\item[7.] Advanced Numerical Analysis
\item[8.] Thesis in Mathematics
\item[9.] Optimization
\end{enumerate}

{\bf Undergraduate Courses}
\begin{enumerate}
\item[1.] Calculus Courses
\item[2.] Differential Equations
\item[3.] Numerical Analysis
\item[4.] Linear Algebra
\item[5.] Real Analysis
\item[6.] History of Mathematics
\item[7.] Geometry
\item[8.] Statistics
\item[9.] Abstract Algebra
\item[10.] Independent Study in Mathematics
\item[11.] Matrix Algebra
\item[12.] Survey of Mathematics
\item[13.] Intermediate Algebra
\item[14.] College Algebra
\end{enumerate}

\newpage %%%
\noindent
(B) {\bf Teaching Effectiveness}

\medskip
I believe that I have had some success in using computer softwares for
some of the applied math courses taught in the department. Since my
research area is in applied mathematics it was not difficult for me to use
existing software as well as produce my own. It has been desirable for
students to use computer softwares as a facilitating tool in many courses.

I have been attending seminars and conferences as well as constantly reviewing
the developments in my field in order to have a broad knowledge of mathematical
subjects. I am trying to be aware of its increasing relevance in our
technological age, and be able to stimulate my students to understand and
possibly use some of these concepts in their future careers.

I am also concerned with the communication of these ideas to students. Throughout
the course I try to make the concepts as understandable as possible by giving
examples that help them relate these ideas to topics in that course. I have also
provided opportunities to my students in which they can express their views to
the class to sharpen their skills in discovering and communicating the concepts.
I have used my teaching effectiveness throughout my teaching career.

I have also produced four textbooks to be used by students in Mathematics,
Economics, Physics, Engineering, and the applied sciences. Several more on the
same areas have been submitted.

I have also reviewed a Numerical Analysis textbook entitled ``Introduction to
Numerical Analysis", by Kendall Atkinson, University of Iowa, published by John
Wiley and Sons (1992). The author in his preface recognizes and praises my talents
in teaching and expresses his gratitude for my contribution in the improvement of
the book. His textbook is considered to be the best book in Numerical Analysis
in this country.

I have assisted several students to be accepted in graduate programs at the
top universities in this country.

I have also helped them find jobs and still keep in contact with them and their
careers after they leave the University.

\bigskip
\noindent
6. {\bf AWARDS, HONORS AND AFFILIATIONS}

\medskip
\noindent
(A) {\bf Conference Chairman}

\medskip
Applied Mathematics Section Annual Meeting of the American Mathematical
Society and Mathematical Association of America meeting, held at San
Francisco, January 1991.

\medskip
\noindent
(B) {\bf Outstanding Graduation Record}

\medskip
I was able to finish both my M.S.\ and Ph.D.\ degrees at the University of
Georgia at the record time of two years which has not been broken yet.

\medskip
\noindent
(C) {\bf National-International Recognition}

\medskip
A total of 91 scientists from five continents have requested reprints of 91\%
of my published works so far.

I have participated in the evaluation process for tenure and promotion by 
several U.S.\ and international universities.

I reviewed several Ph.D.\ theses of students from the United States and overseas
universities.

Member American Mathematical Society

Member Mathematical Association of America

Member Pi Mu Epsilon

Nominated for the Distinguished Faculty Award for 1993 and 1995,
Cameron University

Included in the fourth edition of ``WHO'S WHO AMONG AMERICA'S TEACHERS",
1996. This national organization honors a select 5\% of United States teachers.

\bigskip
\noindent
7. {\bf DEPARTMENTAL SERVICE}

\begin{enumerate}
\item[1.] Member of the graduate studies committee (N.M.S.U.)

\item[2.] Member of the graduate faculty (N.M.S.U.)

\item[3.] I have been asked and provided input to the members of the
departmental personnel committee concerning hiring, updating the math major
and other matters.
\item[4.] I have been serving as a regular advisor to students and have helped
some of them to present papers and give talks at conferences.
\item[5.] See also previous items.
\end{enumerate}

\bigskip
\noindent
8. {\bf UNIVERSITY SERVICE}

\begin{enumerate}
\item[1.] I have been participating in the Cameron Interscholastic Service.

\item[2.] I have been serving some of the Cameron faculty as consultant.
\item[3.] Dean's representative (N.M.S.U.).
\item[4.] See also previous items.
\end{enumerate}

\bigskip
\noindent
9. {\bf STUDENT SERVICE}

\begin{enumerate}
\item[1.] I have been participating in many of our student activities
including Mathematics, Pi Mu Epsilon and CS Club activities.
\item[2.] See also previous items.
\end{enumerate}

\bigskip
\noindent
10. {\bf COMMUNITY SERVICE}

\medskip 
 I have been helping people from Lawton (Fort Sill, Goodyear
plant and others) and surrounding areas with their mathematical problems.

\newpage %%%
\noindent
11. {\bf BRIEF DESCRIPTION OF SOME OF THE BOOKS AS LISTED IN 4(H)}

\medskip
1. {\it The Theory and Applications of Iteration Methods}

\smallskip
This textbook was written for students in engineering, the physical sciences,
mathematics, and economics at an upper division undergraduate or graduate level.
Prerequisites for using the text are calculus, linear algebra, elements of
functional analysis, and the fundamentals of differential equations. Students
with some knowledge of the principles of numerical analysis and optimization
will have an advantage, since the general schemes and concepts can be easily
followed if particular methods, special cases, are already known. However, such
knowledge is not essential in understanding the material of this book.

A large number of problems in applied mathematics and also in engineering are solved
by finding the solutions of certain equations. For example, dynamic systems are
mathematically modeled by differences or differential equations, and their
solutions usually represent the states of the systems. For the sake of simplicity,
assume that a time-invariant system is driven by the equation $\dot{x} =f(x)$,
where $x$ is the state. Then the equilibrium states are determined by solving the
equation $f(x) =0$. Similar equations are used in the case of discrete systems.
The unknowns of engineering equations can be functions (difference, differential,
and integral equations), vectors (systems of linear or nonlinear algebraic
equations), or real or complex numbers (single algebraic equations with single
unknowns). Except in special cases, the most commonly used solution methods are
iterative --- when starting from one or several initial approximations a sequence
is constructed that converges to a solution of the equation. Iteration methods
are also applied for solving optimization problems. In such cases, the iteration
sequences converge to an optimal solution of the problem at hand. Since all of
these methods have the same recursive structure, they can be introduced and
discussed in a general framework.

In recent years, the study of general iteration schemes has included a substantial
effort to identify properties of iteration schemes that will guarantee their
convergence in some sense. A number of these results have used an abstract
iteration scheme that consists of the recursive application of a point-to-set
mapping. In this book, we are concerned with these types of results.

Each chapter contains several new theoretical results and important applications
in engineering, in dynamic economic systems, in input--output systems, in the
solution of nonlinear and linear differential equations, and in optimization problems.

Chapter 1 gives an outline of general iteration schemes in which the convergence
of such schemes is examined. We also show that our conditions are very general:
most classical results can be obtained as special cases and, if the conditions
are weakened slightly, then our results may not hold. In Chapter 2 the discrete
time-scale Liapunov theory is extended to time dependent, higher order, nonlinear
differential equations. In addition, the speed of convergence is estimated in
most cases. The monotone convergence to the solution is examined in Chapter 3
and comparison theorems are proved in Chapter 4. It is also shown that our results
generalize well-known classical theorems such as the contraction mapping principle,
the lemma of Kantorovich, the famous Gronwall lemma, and the well-known stability
theorem of Uzawa. Chapter 5 examines conditions for the convergence of special
single-step methods such as Newton's method, modified Newton's method, and
Newton-like methods generated by point-to-point mappings in a Banach space setting.
The speed of convergence of such methods is examined using the theory of majorants
and a method called ``continuous induction", which builds on a special variant
of Banach's closed graph theorem. Finally, Chapter 6 examines conditions for monotone
convergence of special single-step methods such as Newton's method, Newton-like
methods, and secant methods generated by point-to-point mappings in a partially
ordered space setting.

At the end of each chapter, case studies and numerical examples are presented
from different fields of engineering and economy.

\medskip
3. {\it The Theory and Application of Abstract Polynomial Equations}

\smallskip
My goal in the text is to present new and important old results
about polynomial equations as well as an analysis of general
new and efficient iterative methods for their numerical solution in various very general space settings. To achieve
this goal we made the text as self-contained as possible
by proving all the results in great detail. Exercises have been added at the end of each chapter that complement
the material in the sense that most of them can be considered
really to be results (theorems, propositions, etc.) that we
decided not to include in the main body of each chapter.
Several applications of our results are given for the
solution of integral as well as differential equations
throughout every chapter.

Abstract polynomial equations are evidently systems of algebraic polynomial
equations. Polynomial systems can arise directly in applications, or be
approximations to equations involving operators having a power series
expansion at a certain point. Another source of polynomial systems is the
discretization of polynomial equations taking place when a differential
or an integral equation is solved. Finite polynomial systems can be obtained
by taking a segment of an infinite system, or by other approximation
techniques applied to equations in infinite dimensional space.

We have provided material that can be used on the one
hand as a required text in the following graduate study 
areas: Advanced Numerical Analysis, Numerical Functional
Analysis, Functional Analysis and Approximation Theory.
On the other hand, the text can be recommended for a graduate
integral or differential equations course.
Moreover, to make the work useful as a reference source,
literature citations will be supplied at the end of each
chapter with possible extensions of the facts contained
here or open problems.
We will use graphics and exercises designed to allow students
to apply the latest technology. In addition, the text will
end with a very updated and comprehensive bibliography in
the field. The main prerequisite for the reader is the
material covered in: advanced calculus, second course
in numerical-functional analysis and a first course in
algebra and integral-differential equations.
A comprehensive modern presentation of the subject to be
described here appears to be needed due to the rapid
growth in this field and should benefit not only those
working in the field, but also those interested in, or
in need of, information about specific results or
techniques.

Chapters 1, 2 and 3 cover special cases of nonlinear operator equations. In particular the solution of polynomial operator
equations of positive integer degree $n$ is discussed. The
so-called polynomial operators are a natural generalization
of linear operators. Equations in such operators are the linear
space analog of ordinary polynomials in one or several variables
over the fields of real or complex numbers. Such equations
encompass a broad spectrum of applied problems including all
linear equations. Often the polynomial nature of many
nonlinear problems goes unrecognized by researchers. This is
most likely due to the fact that unlike polynomials in a single
variable, polynomial operators have received little attention. It must certainly be mentioned that existence
theory is far from complete and what little is there is confined to local small solutions in neighborhoods which
are often of very small radius. Here an attempt is made to
partially fill this space by doing the following:

\begin{enumerate}
\item[(a)] Numerical methods for approximating distinct
solutions of quadratic $(n =2)$ (in Chapters 1 and 2) and polynomial
equations $(n \geq 2)$ (in Chapter 3) are given;

\item[(b)] Results on global existence theorems not related
with contractions are provided;
\item[(c)] Moreover for those of a qualitative rather than
computational frame of mind, it has been suggested that
polynomial operators should carry a Galois theory. In an
attempt to inform and contribute in this area we have
provided our results at the end of each chapter.
\end{enumerate}

Chapter 4 deals with polynomial integral as well as polynomial
differential equations appearing in radiative transfer,
heat transfer, neutron transport, electromechanical networks,
elasticity and other areas. In particular, results
on the various Chandrasekhar equations (Nobel Prize of
Physics, 1983) are given using Chapters 1--3. These
results are demonstrated through the examination of different
cases.

In Chapter 5 we study the Weierstrass theorem, Matrix
representations, Lagrange and Hermite interpolation,
completely continuous multilinear operators, and
the bounds of polynomial equations in the following
settings: Banach space, Banach algebra and Hilbert space.
   
Finally in Chapter 6 we provide general methods for solving
operator equations. In particular we use inexact Newton-like
methods to approximate solutions of nonlinear operator
equations in Banach space. We also show how to use
these general methods to solve polynomial equations.


\medskip
6. {\it A Survey of Efficient Numerical Methods and Applications}

\smallskip
Our goal in this textbook is to present a survey of new, and important
old results about equations as well as an analysis of new and efficient
iterative methods for their numerical solution in various space settings.
To achieve this goal, we made the textbook as self-contained as possible
by providing all the results in great detail. Exercises have been added at the
end of each chapter that complement the material. Some of them are results
(Theorems, Propositions, etc.) that we decided not to include in the main
body of each  chapter. Several applications of our results are given for the
solution of integral as well as differential equations throughout every chapter.

We have provided material that can be used by undergraduate students at their
senior year as well as researchers interested in the following study areas:
Advanced Numerical Analysis, Numerical Functional Analysis, Functional Analysis
Approximation Theory, Integral and Differential Equations, and all computational
areas of Engineering, Economics and Statistics. Moreover, we make the work useful
as a reference source, literature citations have been supplied at the end of each
chapter with possible extensions of the facts contained here or open problems.
The exercises are designed to allow readers to apply the latest technology.
In addition, the textbook ends with a very updated and comprehensive bibliography
in the field. The main prerequisite for the reader is the material covered in:
Advanced Calculus, Advanced Course in Analysis, second course in
Numerical-Functional Analysis and a first course in Algebra and Integral-Differential
Equations. A comprehensive modern presentation of the Numerical Methods described
here appears to be needed due to the rapid growth in this field and should
benefit not only those working in the area, but also those interested in, or
in need of, information about specific results or techniques.

We use: (E) to denote an equation of the form
$$
F(x) =0 \eqno({\rm E})
$$
defined on spaces to be specified each time; (N) denotes Newton's method
$$
x_{n +1} =x_n -F'(x_n )^{-1} F(x_n )\quad (n\geq 0), \eqno({\rm N})
$$
notation (S) denotes Secant method
$$
x_{n +1} =x_n - [x_n ,x_{n -1}]^{-1} F(x_n )\quad (n\geq 0),
\eqno({\rm S})
$$
whereas by $[x_n ,x_{n-1}]$ we mean $[x_n ,x_{n -1};F]$; and finally (NL)
denotes Newton-like method
$$
x_{n +1}= x_n -A(x_n )^{-1} F(x_n )\quad (n\geq 0). \eqno({\rm NL})
$$

Chapter 1 serves as an introduction for the rest of the chapters. Topics
related with partially ordered topological spaces are covered here. Moreover,
divided differences in linear as well as in Banach spaces are being discussed.
Furthermore, divided differences, Fr\'echet derivatives, and the relationship
between them is being investigated.

Several unpublished results have also been added demonstrating how to
select divided differences, Fr\'echet derivatives satisfying Lipschitz 
conditions or certain new natural monotone estimates similar but not
identical to conditions already in the literature of the form, e.g.,
$$
[x,y] \leq [u,v] \quad \mbox{for} \ x\leq u \ \ \mbox{and} \ \ y\leq v.
$$
These results are developed, on the one hand because they are needed for the
convergence theorems in Chapters 2--4 that follow, and on the other hand
because they have an interest of their own.

Chapter 2 deals with the following concern: Applying Newton methods to solve
nonlinear operator equations of the form $F(x)=0$ in a Banach space amounts to
calculating two scalar constants and one scalar function over the positive real
line. This is due to the fact that conditions on the Fr\'echet-derivative $F'$
of $F$ of the form
$$
\| F' (x) -F'(y)\| \leq L\| x-y\| , \ \ \mbox{or} \ \| F'(x) -F'(y)\|\leq
K(r)\| x-y\|
$$
or more recently by us $\| F'(x +h)-F' (x)\| \leq A(r,\| h\| )$ for all $x,y$
in a certain ball centered at a fixed point $x_0$, of radius $R>0$ with $0
\leq r\leq R$ and $\| h\| \leq R-r$ have been used for the convergence
analysis to follow. The constants are of the form $a =\| F' (x_0 )^{-1}\|$
and $b = \| F'(x_0 )^{-1} F(x_0)\|$. The task of computing the constants $L$,
$a$, $b$ as well as the functions $K(r)$ and $A(r,t)$ is carried out for
integral operators $F$ in the spaces $X =C$, $L_p$ $(1\leq p <\infty )$ and
$L_\infty$.

After going through the first two chapters, we can undertake the main goal
discussed in the rest of the text.

Chapter 3 covers the problem of approximating a locally (or globally) unique
solution of the operator equation $F(x) =0$ in the following settings: Banach
space, Banach algebra, Hilbert space, Partially ordered Topological and
Euclidean space. In the first four sections, convergence results are given
using Newton (N), Secant (S) as well as Newton-like methods (NL) under conditions
on the divided differences, Fr\'echet derivatives discussed in the first two
chapters. Several results have been provided to improve upon the ones already
in the literature by considering cases. The following have been done:

\begin{enumerate}
\item[(a)] Refined proofs using the same techniques are given;
\item[(b)] Different techniques have been applied;
\item[(c)] New techniques have been used;
\item[(d)] New results have been discovered.
\end{enumerate}

\noindent
In Section 5 the monotone convergence of methods (N), (S) and (NL) is
discussed.

Until Section 5, two classes of convergence theorems are discussed:
theorems of essentially Kantorovich-type and global theorems based on
monotonicity considerations. In Section 5 however a general unifying structure
for the convergence analysis which is strong enough to derive both types
of theorems from a basic theorem is discussed.

In Sections 6 and 7 results on rates of convergence as well as $Q$- and
$R$-orders are being given respectively. Once recent results of others in
this area have been discussed, we show how to improve upon them.

Chapter 4 deals with the problem discussed already in Chapter 3, but
two-step Newton methods are employed as an attempt to improve upon the order
of convergence and achieve the highest possible computational efficiency.
The flow of Chapter 3 is followed here also. In mose cases the superiority
of these over single-step methods is being demonstrated.

\bigskip
\noindent
12. {\bf BRIEF DESCRIPTION OF PAPERS AS LISTED IN 4(I)}

\medskip
The papers concern topics included in the list of research areas listed in
4(I).

The so-called polynomial operators are a natural generalization of linear
operators. Equations in such operators are the linear space analog of ordinary
polynomials in one or several variables over the fields of real or complex
numbers. Such equations encompass a broad spectrum of applied problems including
all linear equations. Often the polynomial nature of many non-linear problems
goes unrecognized by researchers. This is most likely due to the fact that
unlike polynomials in a single variable, polynomial operators have received
little attention. Whether this situation is due to an inherent intractability
of these operators or to simple oversight remains to be seen. Hopefully, one
should be able to exploit their semi-linear character to wrest more extensive
results for these equations than one can obtain in the general non-linear setting.

Examples of equations involving polynomial operators can be found in the
literature. My contribution in this area can be found in papers \#3, 4,
6--12, 16, 22, 23, 25, 35, 84. Many of the equations of elasticity theory are
of this type \#3, 4. The problem discussed there pertains to the buckling of a
thin shallow spherical shell clamped at the edge and under uniform external
pressure.

Some equations in heat transfer, kinetic theory of gases and neutron transport,
including the famous S.\ Chandrasekhar (Nobel in Physics, 1983) integral equation
are of quadratic type. Numerical methods for finding small or large solutions
of the above equations and their variations as well as results on the number
of solutions of the above equations can be found in papers \#1--4, 21, 24, 37,
55, 85, 99.

Some pursuit and bending of beams problems can be formulated as polynomial
equations. My investigations on such equations can be found in paper \#6.

Paper \#11 contains results on the study of feedback systems containing an
arbitrary finite number of time-varying amplifiers and the study of
electromechanical networks containing an arbitrary number of time-varying
nonlinear dissipative elements.

Scientists that have worked in this area agree that much work, both of
theoretical and computational nature, remains to be done on polynomials
in a normed linear space. A summary of some of the remaining problems can
be found in my second and third book (see 4(G)).

It must certainly be mentioned that the existence theory is far from
complete and what little is there it is confined to local small solutions in
neighborhoods which are often of very small radius \#1--5, 7--9, 13, 14, 17,
26, 30, 33. In my papers \#5, 6, 8, 10, 23, 30, 33, 34, 37, 42, 69, 72, I have
provided numerical methods for approximating distinct solutions of polynomial
equations under various hypotheses.

As far as I know the above-mentioned authors are the only researchers that
have worked on global exitence theorems not related with contractions. My
contribution in this area is contained in papers \#7, 14, 23, 34, 35, 44, 69.

Moreover for those of a qualitative rather than computational frame of mind,
it has been suggested that polynomial operators should carry a Galois theory.
Such a theory, should it exist, may be very limited, but nonetheless, interesting.
The pessimistic note is prompted by the fact that a complete general spectral
theory does not exist for polynomial operators. In an attempt to produce such
a theory at least the way an analyst understands it, I wrote the relevant papers
\#18, 23, 34, 35, 45.

The most important iterative procedures for solving nonlinear equations in
a Banach space are undoubtedly the so-called Newton-like methods. Indeed, 
L.V.\ Kantorovich has given sufficient conditions for the quadratic convergence
of Newton's iteration to a locally unique solution of the abstract nonlinear
equation in Banach space. His conditions are in some sense the best possible.
For the scalar case these conditions coincide with those given earlier by A.I.\
Ostrowski. Simple sharp apriori estimates were given independently (by different
methods) by W.B.\ Gragg and R.A.\ Tapia. The method of nondiscrete mathematical
induction was used later by V.\ Ptak, F.\ Potra, X.\ Chen, T.\ Yamamoto, P.\
Zabrejko, D.\ Ngyen, I.\ Moret et al.; this method yields not only sharp 
apriori estimates but also convergence proofs through the induction theorem.
This method, in which the rate of convergence is now a function and not a
number, is closely related with the closed graph theorem. My contribution in
this area can be found in the papers \#19, 20, 31, 40, 44, 50, 51, 57, 60, 61,
63, 65, 68, 70, 81, 82, 83, 89, 90, 92, 95, 96, 97, 101, 125, 129, 145.

One of the basic assumptions for the use of Newton's method is the condition
that the Fr\'echet derivative of the nonlinear operator involved be
Fr\'echet-differentiable. There are however interesting differential equations
and singular integral equations (see, for example, the work of Etzio Venturino)
where the nonlinear operator is only H\"older continuous. It turns out that the
error analysis of Newton-like methods changes dramatically and the results
obtained by the above authors do not hold in this setting. My contribution in
this area can be found in the papers \#19, 20, 31, 32, 38, 63, 68, 71, 100.

Papers \#65, 73, 104, 106 deal with the solutions of nonlinear operator equations
containing a nondifferentiable term.

Papers \#61, 80, 89, 101, 104, 113 deal with the approximation of implicit functions.

Papers \#60, 66, 79, 81, 95, 104 deal with projection methods for the
approximate solution of nonlinear equations.

Papers \#64, 125, 143 deal with iterative procedures for the solution
of nonlinear equations in generalized Banach spaces.

Papers \#88, 114, 128, 130, 152 deal with inexact iterative procedures.

Papers \#54, 56, 67, 98, 124 deal with the solution of nonlinear operator
equations and their discretizations in relation with the mesh-independence
principle.

Papers \#82, 105, 116 deal with the solution of linear and nonlinear
perturbed two-point boundary value problems with left, right and interior
boundary layers.

I have applied the above numerical methods, in particular Newton's and its
variations to concrete integral equations arising in radiative transfer.
See, for example, papers \#21, 37.
Since the numerical solution of integral equations is closed related to
compact operators, I tried in the papers \#28, 39, 53, 74 to find some
results relating numerical methods and compactness. Work on this subject
has already been conducted (see, e.g., the work of P.\ Anselone and K.\
Atkinson), but the results so obtained are too general or too particular
to be used for my purposes.

Papers \#91, 121, 131, 132, 133, 138, 140, 149, 153--218
deal with the convergence and error analysis of multipoint iterative methods
in Banach spaces.

Paper \#103 deals with the introduction of an optimization algorithm based
on the gradient projection technique and the Karmarkar's projective scaling
method for linear programming.

Paper \#123 (statistics) deals with t-estimates of parameters of general
nonlinear models in finite dimensional spaces. The method is highly
insensitive to outliers. It can also be applied to solve a system of
nonlinear equations.

Papers \#62, 74, 76, 93, 94, 107, 134, 139 (mathematical economics)
deal with the convergence of iteration schemes generated by the recursive
application of a point-to-set mapping. Our results have been applied
to solve dynamic economic as well as input--output systems.

The rest of the papers involve  nondifferentiable
operator equations on genealized Banach spaces with a convergence
structure and inexact Newton methods, as well as iterative procedures using
outer or generalized inverses. Globally convergent inexact Newton methods
have also been studied. In particular sufficient conditions have been imposed
on the residuals in order to achieve the usual orders of convergence.
We have observed that error bounds can be improved and the radius of
convergence for Newton's method can be enlarged if the Fr\'echet
derivative of the operator involved is sufficiently many times
differentiable.






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