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1. PERSONAL

 PLACE OF BIRTH Department of Mathematics 
NAME: 		 Ioannis K. Argyros



PLACE OF BIRTH:			 Athens, Greece



ADDRESS: 		 Cameron University

 		 Department of Mathematics

 		 Lawton, OK 73505 USA



E-MAIL: 		 ioannisa@cameron.edu



FAX:			 (580) 581-2616



TELEPHONE: 		 (580) 581-2908 or (580) 581-2481 (Office)

 		 (580) 536-8754 (Home)

2. STUDIES

PLACE OF BIRTH Department of Mathematics (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

3. ACADEMIC EXPERIENCE

 PLACE OF BIRTH Department of Mathematics 
(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

4. SCIENTIFIC ACTIVITY

(A) Fields of Interest/Research Has Been Conducted In:

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.

(B) Editing

1.: I am the co-founder and Editor-in-Chief of the Southwest Journal of Pure and Applied Mathematics. This is a peer-reviewed purely electronic journal established in 1995 at Cameron University
2.: Editor of the Korean Journal of Computational and Applied Mathematics
3.: Editor of the journal Computational Analysis and Applications (Plenum Publ.)
4.: Editor of the journal Advances in Nonlinear Variational Inequalities (ANVI) (International Publications, USA)

1.: Elementary Numerical Analysis by Kendall Atkinson, University of Iowa, published in 1992 by John Wiley and Sons.
2.: Moduli of Continuity and Global Smoothness Preservation in Approximation Theory by G.A. Anastassiou and Sorin G. Gal. Reviewed for Springer-Verlag Publishers, World Scientific Publishing Company, Elsevier Science B.V., Birkhauser, and CRC Press.
3.: A Handbook on Analytic-Computational Methods and Applications, by G.A. Anastassiou. Reviewed for Plenum Publ., Corp., World Scientific Publishing Company.

(D) Scientific Papers Reviewer

I have reviewed a total of 158 papers for:

1.: Journal of Computational and Applied Mathematics
2.: P.U.J.M.
3.: Mathematica Slovaca
4.: Pure Mathematics and Applications (PUMA)
5.: Southwest Journal of Pure and Applied Mathematics
6.: IMA Journal of Numerical Analysis
7.: Journal of Optimization Theory and Its Applications
8.: Computer Physcis Communications
9.: SIAM Journal Numerical Analysis
10.: Computational and Applied Mathematics, CAM 97, 98, Edmond, OK, USA
11.: Applied Mathematics Letters
12.: Illinois Journal of Mathematics
13.: Korean Journal Computational and Applied Mathematics
14.: Proceeding of the Cambridge Mathematical Society
15.: Applicable Analysis
16.: Journal of Applied Mathematics and Optimization
17.: Computers and Mathematics with Applications
18.: Computational and Applied Mathematics
19.: Computational Analysis and Applications
20.: Tamkang Journal of Mathematics
21.: Soochow Journal of Mathematics
22.: Portugaliae Mathematica
23.: Aequationes Mathematicae

(E) Grants Received

1.: New Mexico State University Grant, (1986), #1-3-43841, RC #87-01
2.: New Mexico State University Grant, (1987), #1-3-4-44770.
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"
4.: Cameron University, Research support, July 1992, June 1998

(F) Supervising Graduate Students

The following Ph.D. students have obtained their Ph.D. degree under my supervision:

1.: Losta Mansor, Ph.D. dissertation title: Numerical Methods for Solving Perturbation Problems Appearing in Elasticity and Astrophysics, 1989
2.: Joan Peeples, Ph.D. dissertation title: Point to Set Mappings and Oligopoly Theory, 1989.

Member, Doctoral Examination Committee:

3.: Aomar Ibenbrahim, Spring 1987
4.: Maragoudakis Christos, Spring 1988
(Dean's Representative for both, Electrical Engineering Department)
5.: Bellal Hossain, Fall 1996 University of Calcutta, India
6.: Sri Pulak Guhathakurta, Spring 1998, University of Calcutta, India

Chair, Master's Examination Committee

7.: Mitra Ashan, Spring 1987
8.: Christopher Stuart, Spring 1988
9.: Anis Shahrour, Fall 1988

Member, Master's Examination Committee

10.: Juji Hiratsuka, Spring 1987 (Dean's Representative, Art Department)
11.: Alice Lynn Bertini, Spring 1988
12.: Daniel Patrick Eshner, Summer 1989 (Dean's Representative, Computer Science)

(G) Committee Member for Hiring-Promotion-Tenure

I have served as a committe member for:

(a): Hiring: Cameron University (USA), PUNJAB University (Pakistan)
(b): Promotion-Tenure: Cameron University (USA), Sultan Qaboos University, Sultanate of Oman, Sam Houston State University (USA)

(H) Books Published

1.: 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.
2.: 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.
3.: A Survey of Efficient Numerical Methods for Solving Equations and Applications, Kyung Moon Publishers, Seoul, Korea, 1999.
4.: Comprehensive Dictionary of Mathematics: Analysis Calculus and Differential Equations, Chapman-Hall/CRC/Lewis Publishers, Boca Raton, Florida, USA, 1999.
5.: Computational Methods for Abstract Polynomial Equations, Monografii Mathematicae,
Timisoara, Romania, 1997.

Books Submitted for Publication

6.: A Unified Approach for Solving Equations, Part I: On Infinite Dimensional Spaces.
7.: A Unified Approach for Solving Equations, Part II: On Finite Dimensional Spaces.
8.: Approximate Solutions of Nonlinear Operator Equations in Abstract Spaces and Applications.
9.: Iterative Methods for the Solution of Equations and Applications.

(I) Research Articles

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

America: U.S.A., Canada, Chile

Europe: U.K., Sweden, Belgium, Holland, Spain, Germany, Austria, Hungary, Slovakia, Romania, Poland, Yugoslavia, Italy

Asia: People's Republic of China, Republic of China, India, Pakistan, Japan, Saudi Arabia, Korea

Australia: Australia

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).

1.: A Contribution to the Theory of Nonlinear Operator Equations in Banach Space, Master of Science Dissertation, 1983.
2.: Quadratic Equations in Banach Space, Perturbation Techniques and Applications to Chandrasekhar's and Related Equations, Doctor of Philosophy Dissertation, 1984.
3.: Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc., Vol. 32, 2 (1985), 275-292; Not. Amer. Math. Soc., 85T-46-142; Z.F.M.6074063 (1987); Math. Rev. 87d: Gerard Lebourg (Paris).
4.: On a contraction theorem and applications, Proc. Amer. Math. Soc., Symposium on Nonlinear Functional Analysis and Applications, 45, 1 (1986), 51-53; Math. Rev. 87h: 65108, Sh. Singh, Z.F.M.6224077 (1988).
5.: Iterations converging to distinct solutions of some nonlinear equations in Banach space, Internat. J. Math. & Math. Sci., Vol. 9, No. 3 (1986), 585-587; Z.F.M.61447044 (1986); Math. Rev. 87j47097, P.P. Zabrejko (Minsk).
6.: On the cardinality of solutions of multilinear differential equations and applications, 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.
7.: Uniqueness-Existence of solutions of polynomial equations in linear space, P.U.J.M., Vol. XIX (1986), 39-57; Z.F.M.62547050 (1988); Math. Rev. 88g47116, B.G. Pachpatte (6-Mara).
8.: On a theorem for finding ``large" solutions of multilinear equations in Banach space, P.U.J.M., Vol. XIX (1986), 29-37; Z.F.M.62547051 (1988); Math. Rev. 88g47115, B.G. Pachpatte (6-Mara).
9.: On the approximation of some nonlinear equations, Aequationes Mathematicae, 32 (1987), 87-95; Z.F.M.61447043 (1986); Math. Rev. 88g47124, P.P. Zabrejko (Minsk).
10.: An improved condition for solving multilinear equations, P.U.J.M., Vol. XX (1987), 43-46; Math. Rev. 89c47065; Z.F.M.64747015, (1989).
11.: On a class of nonlinear equations, 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.
12.: On polynomial equations in Banach space, perturbations, techniques and applications, Internat. J. Math. & Math. Sci., Vol. 10, No. 1 (1987), 69-78; Math. Rev. 88c47123, Heinrich Steinlein (Munich); Z.F.M.61747038, (1987).
13.: A note on quadratic equations in Banach space, P.U.J.M., Vol. XX (1987), 47-50; Math. Rev. 89c47076; Z.F.M.64747016, (1989).
14.: Quadratic finite rank operator equations in Banach space, Tamkang J. Math., Vol. 18, No. 4 (1987); 8-19; Z.F.M.66247011 (89); Math. Rev. 89k47100, Nicole Brillouet-Belluot (Nantes).
15.: On some theorems of Mishra Ciric and Iseki, Mat. Vesnik, Vol. 39 (1987), 377-380; Math. Rev. 89c54083; Z.F.M.64854035, (1989).
16.: An iterative solution of the polynomial equation in Banach space, Bull. Inst. Math. Acad. Sin., Vol. 15, No. 4 (1987), 403-410; (Math. Rev. Author index 1989), 47H17, 46G99, 58C15.
17.: A survey on the ideals of the space of bounded linear operators on a separable Hilbert space, Rev. Acad. Ci. Exactas Fis. Quim. Nat. Zaragoza, II. Ser. 42 (1987), 24-43; Math. Rev. 89g47059.
18.: On the solution by series of some nonlinear equations, 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).
19.: Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc., Vol. 37, 1 (1988), 131-147; Z.F.M.62965061, (1988), S. Reich; Math. Rev. 89b65142, A.V. Dzhishkariani (Tbilisi).
20.: On Newton's method and nondiscrete mathematical induction, Bull. Austral. Math. Soc., Vol. 38 (1988), 131-140; Math. Rev. 90a65136, A.M. Galperin (Ben-Gurion Intern. Airp.).
21.: On a class of nonlinear integral equations arising in neutron transport, Aequationes Mathematicae, Vol. 35 (1988), 99-111; Math. Rev. 89M47058, H.E. Gollwitzer (1-DREX).
22.: On multilinear equations, Pr. Rev. Mat., Vol. 14 (July 1988), 95-105.
23.: New ways for finding solutions of polynomial equations in Banach space, Tamkang J. Math., Vol. 19, 1 (1988), 37-42; Math. Rev. 90f47093, V.V. Vasin (Sverdlosk).
24.: On a new iteration for solving the Chandrasekhar's H-equations, Pr. Rev. Mat., No. 15 (1988), 21-31.
25.: On a new iteration for solving polynomial equations in Banach space, Funct. et Approx. Comment. Math., Vol. XIX (1988); Math. Rev. 91d:65082, Xiaojun Chen.
26.: Conditions for faster convergence of contraction sequences to the fixed points of some equations in Banach space, Tamkang J. Math., Vol. 19, 3 (1988), 19-22; Math. Rev. 90j47074, Roman Manka (Mogilno).
27.: On some nonlinear equations, Pr. Rev. Mat., No. 15 (1988), 75-82.
28.: On the approximation of solutions of compact operator equations, PR. Rev. Mat., Vol. 14, (July 1988), 29-46.
29.: Approximating the fixed points of some nonlinear equations, Mathem. Slovaca, 38, No. 4 (1988), 409-417; Z.F.M.667 (1989), S.L. Singh. Math. Rev. 90g47109 (O.P. Kapoor (6-11TK)).
30.: Some sufficient conditions for finding a second solution of the quadratic equation in Banach space, Mathem. Slovaca, 4 (1988); Math. Rev. 90g47108 (O.P. Kapoor (6-11TK)).
31.: Concerning the approximation solutions of operator equations in Hilbert space under mild differentiability conditions, Tamkang J. Math., Vol. 19, No. 4 (1988), 81-87; Math. Rev. 91g:65137, P.S. Milojevic.
32.: The Secant method and fixed points of nonlinear equations, Monatshefte fur Mathematik, 106 (1988), 85-94; Z.F.M.65265043 (1989); Math. Rev. 90b6511, A.M. Galperin, Ben-Gurion Intern. Airport.
33.: An iterative procedure for finding ``large" solutions of the quadratic equation in Banach space, P.U.J.M., Vol. XXI (1988), 13-21; Math. Rev. 91g:65136, P.S. Milojevic.
34.: Vietta-Like relations in Banach space, Rev. Acad. Ci. Exactas Fis. Quim. Nat. Zaragoza, I, Ser. 43 (1988), 103-107; Math. Rev. 47f47095, V.V. Vasin (Sverdlovsk).
35.: A global theorem for the solutions of polynomial equations, Rev. Acad. Ci. Exactas Fis. Quim. Nat. Zaragoza, I, Ser. 43 (1988), 93-101; Math. Rev. 90f47094, V.V. Vasin, (Sverdlosk).
36.: Concerning the convergence of Newton's method, P.U.J.M., Vol. XXI (1988), 1-11; Math. Rev. 91g:65135, P.S. Milojevic.
37.: On the number of solutions of some integral equations arising in radiative transfer, Internat. J. Math. & Math. Sci., Vol. 12, No. 2 (1989), 297-304; Math. Rev. 90h86004, S. Rajasekar (Ticuchirapalli).
38.: On the approximate solutions of operator equations in Hilbert space under mild differentiability conditions, J. Pure & Appl. Sci., Vol. 8, No. 1 (1989), 51-56.
39.: On the fixed points of some compact operator equations, Tamkang J. Math., Vol. 20, No. 3 (1989), 203-209; Math. Rev. 91a47088, Jing Xian Sum (PRC-Shan).
40.: Error bounds for a certain class of Newton-like methods, Tamkang J. Math., Vol. 20, No. 4 (1989); Math. Rev. 91k:65096, J.W. Schmidt.
41.: On a generalization of fixed and common fixed point theorems of operators in complete metric spaces, Rev. Mat. Cubo, 5 (1989), 17-25.
42.: Approximating distinct solutions of quadratic equations in Banach space, Rev. Mat. Cubo, 5 (1989), 1-16.
43.: Concerning the convergence of iterates to fixed points of nonlinear equations in Banach space, Bull. Malays. Math. Soc., Vol. 12, 2 (1989), 15-24; Math. Rev. Author index 1991.
44.: A series solution of the quadratic equation in Banach space, Chinese J. Math., Vol. 27, No. 4 (1989); Math. Rev. 90k47131.
45.: On a fixed point in a 2-Banach space, Rev. Acad. Ciencias, Zaragoza, 44 (1989), 19-21; Math. Rev. 91a47077; Math. Rev. 91a:47077.
46.: Some matrices in oligopoly theory, New Mexico J. Sci., 29, 1 (1989), 22.
47.: On a theorem of Fisher and Khan, Rev. Acad. Ciencias, Zaragoza, 44 (1989), 13-17; Math. Rev. 91d:54048, Sehie Park.
48.: On quadratic equations, Mathematica-Rev. Anal. Numer. Theor. Approximation, 18, 1 (1989), 19-26; Math. Rev. 91f:47094.
49.: Concerning the approximate solutions of nonlinear functional equations under mild differentiability conditions, Bull. Malays. Math. Soc., Vol. 12, 1 (1989), 55-65; Math. Rev. 91k:47164, V.V. Vasin.
50.: On the convergence of certain iterations to the fixed points of nonlinear equations, Annales sectio computatorica, Ann. Univ. Sci. Budapest. Sect. Computing, 9 (1989), 21-31; Math. Rev. 91k:65095, J.W. Schmidt.
51.: On the secant method and nondiscrete mathematical induction, Mathematica-Revue D'analyse Numerique et de theorie de l'approximation tome, 18, No. 1 (1989), 27-36; Math. Rev. 91j:65104.
52.: On Newton's method for solving nonlinear equations and multilinear projections, Functiones et approximatio Comment. Math., XIX (1990), 41-52; Math. Rev. 92b:4707, Joe Thrash.
53.: Nonlinear operator equations and pointwise convergence, Functiones et approximatio Comment. Math., XIX (1990), 29-39; Math. Rev. 92b:47106, Joe Thrash.
54.: Iterations converging faster than Newton's method to the solutions of nonlinear equations in Banach space, Functiones et approximatio Comment. Math., XIX (1990), 23-28; Math. Rev. 91m:65164.
55.: On some quadratic integral equations, Functiones et Approximmatio, XIX (1990), 159-166; Math. Rev. 92d:47081, Aeinrich Steinlein.
56.: A mesh independence principle for nonlinear equations using Newton's method and nonlinear projections, Rev. Acad. Ciencias. Zaragoza, 45 (1990), 19-35; Math. Rev. 92e:65076a, Mihai Turinci.
57.: Error bounds for the modified secant method, BIT, 30 (1990), 92-100; Math. Rev. 91d:65083, Xiaojun Chen.
58.: Improved error bounds for a certain class of Newton-like methods, J. Approximation Theory and its Applications, (6:1) (1990), 80-98; Math. Rev. 92a:65188, A.M. Galperin.
59.: On the solution of some equations satisfying certain differential equations, P.U.J.M., Vol. XXIII (1990), 47-59; Math. Rev. 92d:65102.
60.: On some projection methods for approximating the fixed points of nonlinear equations in Banach space, Tamkang J. Math., Vol. 21, 4 (1990), 351-357; Math. Rev. 92a:47072, Joe Thrash.
61.: On some projection methods for the approximation of implicit functions, Appl. Math. Lett., Vol. 3, No. 2 (1990), 5-7; Math. Rev. 91b65066.
62.: On the monotone convergence of some iterative procedures in partially ordered Banach spaces, Tamkang J. Math., Vol. 21, No. 3 (1990), 269-277; Math. Rev. 91h:47067, Joe Thrash.
63.: The Newton-Kantorovich method under mild differentiability conditions and the Ptak error estimates, Monatschefte fur Mathematik, Vol. 109, No. 3 (1990); Math. Rev. 91k:65034, J.W. Schmidt.
64.: The secant method in generalized Banach spaces, Appl. Math. & Comput., 39 (1990), 111-121; Math. Rev. 91h:65099.
65.: On the solution of equations with nondifferentiable operators and Ptak error estimates, BIT, 30 (1990), 752-754; Math. Rev. 91k:65099.
66.: On some projection methods for enclosing the root of a nonlinear operator equation, P.U.J.M., Vol. XXIII (1990), 35-46; Math. Rev. 91h:47067, Joe Thrash.
67.: A mesh independence principle for operator equations and their discretizations under mild differentiability conditions, Computing, 45 (1990), 265-268; Math. Rev. 91i:65106.
68.: On Newton's method under mild differentiability conditions, Arabian J. Math., Vol. 15, 1 (1990), 233-239; Math. Rev. 91k:65097, J.W. Schmidt.
69.: Remarks on quadratic equations in Banach space, Intern. J. Math. & Math. Sci., Vol. 13, No. 3 (1990), 611-616; Math. Rev. 91e:47062.
70.: On the improvement of the speed of convergence of some iterations converging to solutions of quadratic equations, Acta Math. Hungarica, Vol. 57/3-4 (1990), 245-252; Math. Rev. 93d:47121, Teodor Potra.
71.: A note on Newton's method, Rev. Acad. Ciencias Zaragoza, 45 (1990), 37-45; Math. Rev. 92e:65076b, Mihai Turinici.
72.: On the solution of compact linear and quadratic operator equations in Hilbert space, Rev. Acad. Ciencias Zaragoza, 45 (1990), 47-52; Math. Rev. 92e:65076c, Mihai Turinici.
73.: On some generalized projection methods for solving nonlinear operator equations with a nondifferentiable term, Bull. Malays. Math. J., Vol. 13, No. 2 (1990), 85-91; Math. Rev. 92g:65065, Gerard, Lebourg.
74.: Comparison theorems for algorithmic models, Applied Math. and Comput., Vol. 40, No. 2 (Nov. 1990), 179-187; Math. Rev. 92b:65102.
75.: On an iterative algorithm for solving nonlinear equations, Beitrage zur Numerischen Math. (Renamed Z.A.A.), Vol. 10, No. 1 (1991), 83-92; Math. Rev. 93b:47132.
76.: On time dependent multistep dynamic processes with set valued iteration functions on partially ordered topological spaces, Bull. Austral. Math. Soc., Vol. 43 (1991), 51-61; Math. Rev. 92d:65107, Tetsuro Yamamoto.
77.: Error bounds for the secant method, Math. Slovaca, Vol. 41, 1 (1991), 69-82; Math. Rev. 92j:65086, K. Bohmer.
78.: On the approximate solutions of nonlinear functional equations under mild differentiability conditions, Acta Math. Hungarica, Vol. 58 (1-2) (1991), 3-7; Math. Rev. Author index, 1992.
79.: On the convergence of some projection methods with perturbation, J. Comput. and Appl. Math., 36 (1991), 255-258; Math. Rev. 92f:65065, H.R. Shen.
80.: On an application of a modification of the Zincenko method to the approximation of implicit functions, Z.A.A., 10 3 (1991), 391-396; Math. Rev. 93b:47133, Tetsuro Yamamoto.
81.: On some projection methods for solving nonlinear operator equations with a nondifferentiable term, Rev. Academia de Ciencias, Zaragoza, 46 (1991), 17-24; Math. Rev. 92m:47133.
82.: Integral equations for two-point boundary value problems, Rev. Academia de Ciencias, Zaragoza, 46 (1991), 25-35; Math. Rev. 93b:65205, Jan Pekar.
83.: A fixed point theorem for orbitally continuous functions, Pr. Rev. Mat., Vol. 10, No. 7 (1991), 53-57; Math. Rev. 93d:47101, Ramendra Krishna Bose.
84.: Bounds for the zeros of polynomials, Rev. Academia de ciencias, Zaragoza, 47 (1992), 61-66; Math. Rev. 94a:26035, N.K. Govil.
85.: On a class of quadratic equations with perturbation, Functiones et Approximmatio, XX (1992), 51-63; Math. Rev. 94a:45011, P.M. Gupta.
86.: On a new iteration for finding ``almost" all solutions of the quadratic equation in Banach space, Studia Scientiarum Mathematicarum Hungarica, 27, (3-4) (1992), 361-368; Math. Rev. 94d:65037, J.W. Schmidt.
87.: A Newton-like method for solving nonlinear equations in Banach space, Studia Scientiarum Mathematicarum Hungarica, 27 (3-4) (1992), 369-378; Math. Rev. 94d:65038, J.W. Schmidt.
88.: On the convergence of nonstationary Newton methods, Func. et Approx., Vol. XXI (1992), 7-16; Math. Rev. 95g:65080, A.M. Galperin.
89.: On an application of the Zincenko method to the approximation of implicit functions, Publicationes Mathematicae Debrecen, Vol. 40/1-2 (1992), 43-49; Math. Rev. 93c:47076, A.M. Galperin.
90: Improved error bounds for the modified secant method, Intern. J. Computer Math., Vol. 43, No. 1+2 (1992), 99-109.
91.: On the midpoint method for solving nonlinear operator equations in Banach spaces, Appl. Math. Letters, Vol. 5, No. 4 (1992), 7-9; Math. Rev. 96b:65061.
92.: On an application of a Newton-like method to the approximation of implicit functions, Math. Slovaca, 42, No. 3 (1992), 339-347; Math. Rev. 93h:65081, J.W. Schmidt.
93.: On the monotone convergence of general Newton-like methods, Bull. Austral. Math. Soc., 45 (1992), 489-502; Math. Rev. 93c:65077, A.G. Kartsatos.
94.: Convergence of general iteration schemes, J. Math. Anal. and Applic., 168, No. 1 (1992), 42-62; Math. Rev. 93d:65055, S. Sridhar.
95.: Some generalized projection methods for solving operator equations, Journ. Comp. Appl. Math., 39, No. 1 (1992), 1-6; Math. Rev. 92m:65079.
96.: Sharp error bounds for a class of Newton-like methods under weak smoothness assumptions, Bull. Austral. Math. Soc., 45 (1992), 415-422; Math. Rev. 93c:65076, A.G. Kartsatos.
97.: Approximating Newton-like procedures, Appl. Math. Lett., Vol. 5, No. 1 (1992), 27-29.
98.: On a mesh independence principle for operator equations and the secant method, Acta Math. Hungarica, 60, 1-2 (1992), 7-19; Math. Rev. 94g:65057, A.M. Galperin.
99.: On the solution of quadratic integral equations, P.U.J.M., Vol. XXV (1992), 131-143; Math. Rev. 95j:65177, P. Uba.
100.: The secant method under weak assumptions, Proceedings CAM 92, Edmond, OK, (June 1992), 7-18.
101.: On the convergence of generalized Newton-methods and implicit functions, Journ. Comp. Appl. Math., 43 (1992), 335-342; Math. Rev. 93m:65076, J.W. Schmidt.
102.: On a Stirling-like method, P.U.J.M., Vol. XXV (1992), 83-94; Math. Rev. 95j:65062, Anton Suhadolc.
103.: An algorithm for solving nonlinear programming problems using Karmarkar's technique, Proceedings CAM 92, Edmond, OK, (June 1992), 287-296.
104.: On the approximate construction of implicit functions and Ptak error estimates, P.U.J.M., Vol. XXV (1992), 95-98; Math. Rev. Author Index 1995.
105.: On the numerical solution of linear perturbed two-point boundary value problems with left, right and interior boundary layers, Arabian J. Science and Engineering, 17: 4B (October 1992), 611-624; Math. Rev. 94c:65097.
106.: On the convergence of Newton-like methods, Tamkang J. Math., Vol. 23, No. 3 (1992), 165-170; Math. Rev. 93m:65077, J.W. Schmidt.
107.: On the monotone convergence of algorithmic models, Applied Math. and Comput., 48, (2-3) (1992), 167-176; Math. Rev. 92m:47134, Vincentiu Dumitru.
108.: Approximating Newton-like iterations in Banach space, P.U.J.M., Vol. XXV (1992), 49-59; Math. Rev. 95j:65061, Anton Suhadolc.
109.: On the approximation of quadratic equations in Banach space using finite rank operators, Rev. Academia de ciencias Zaragoza, 47 (1992), 67-76; Math. Rev. 94f:47085.
110.: Remarks on the convergence of Newton's method under Holder continuity conditions, Tamkang J. Math., Vol. 23, No. 4 (1992), 269-277; Math. Rev. 94b:65080, J.W. Schmidt.
111.: On the solution of nonlinear operator equations in Banach space and their discretizations, Pure Mathematics and Applications, Ser. B, Vol. 3, No. 2-3-4 (1992), 157-173; Math. Rev. 94i:65069, C.. Ilioi.
112.: On the convergence of optimization algorithms modeled by point-to-set mappings, Pure Mathematics and Applications, Ser. B, Vol. 3, No. 2-3-4 (1992), 77-86; Math. Rev. 94i:90117, Han Ch'ing Lai.
113.: On an application of a modification of a Newton-like method to the approximation of implicit functions, Bull. Malays Math. Soc., Vol. 16, 1 (1993), 25-32.
114.: On the convergence of inexact Newton-like methods, Public. Math. Debrecen, Vol. 43, 1-2 (1993), 79-85; Math. Rev. 94h:65064, Carl T. Kelley.
115.: On some projection methods for the solution of nonlinear operator equations with nondifferentiable operators, Tamkang J. Math., Vol. 24, No. 1 (1993), 1-8; Math. Rev. 94m:65097, A.V. Dzhishkariani.
116.: An initial value method for solving singular perturbed two-point boundary value problems, Arabian Journ. Scienc. and Engineer., Vol. 18, 1 (1993), 3-5.
117.: On the solution of nonlinear equations with a nondifferentiable term, 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).
118.: Some methods for finding error bounds for Newton-like methods under mild differentiability conditions, Acta Math. Hungarica, 61, (3-4) (1993), 183-194; Math. Rev. 94m:65096, A.V. Dzhishkariani.
119.: On the secant method, Publicationes Mathematicae Debrecen, Vol. 43, 3-4 (1993), 223-238; Math. Rev. 95j:47077, R. Kodnar.
120.: Improved error bounds for Newton's method under generalized Zabrejko-Nguen-type assumptions, Appl. Math. Letters, Vol. 6, No. 3 (1993), 75-77; Math. Rev. Author index 1996.
121.: A fourth order iterative method in Banach spaces, Appl. Math. Letters, Vol. 6, No. 4 (1993), 97-98; Math. Rev. Author index 1996.
122.: Newton-like methods and nondiscrete mathematical induction, Studia Scientiarum Mathematicarum Hungarica, 28 (1993), 417-426; Math. Rev. 95b:47084, A.M. Galperin.
123.: Robust estimation and testing for general nonlinear regression models, Appl. Math. and Comp., 58 (1993), 85-101; Math. Rev. 94i:62097, Adrej Pazman.
124.: A mesh independence principle for nonlinear operator equations in Banach space and their discretizations, Studia Scientiarum Math. Hung., 28 (1993), 401-415; Math. Rev. 95b:65077, A.M. Galperin.
125.: Sharp error bounds for the secant method under weak assumptions, P.U.J.M., Vol. XXVI (1993), 54-62; Math. Rev. Author index 1995.
126.: An error analysis of Stirling's method in Banach spaces, Tamkang J. Math., Vol. 24, No. 2 (1993), 115-133; Math. Rev. 94h:65058, A.M. Galperin.
127.: New sufficient conditions for the approximation of distinct solutions of the quadratic equation in Banach space, Tamkang J. Math., Vol. 24, No. 4 (1993), 355-372; Math. Rev. 95f:47090.
128.: On the convergence of inexact Newton methods, Chinese J. Math., Sept. Vol. 21, No. 3 (1993), 227-234; Math. Rev. 94f:47088, Mihai Turinici.
129.: On the solution of equations with nondifferentiable operators, Tamkang J. Math., Vol. 24, No. 3 (1993), 237-249; Math. Rev. 94i:65070, C. Ilioi.
130.: Sufficient conditions for the convergence of general iteration schemes, Chinese J. Math., Vol. 21, No. 2 (1993), 195-205; Math. Rev. 94f:47087, Mihai Turinici.
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; P.U.J.M., Vol. 27 (1994), 23-33; Rev. Academia de Ciencias, Zaragoza, 50 (1995), 5-13; Math. Rev. Author index 1996.
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; P.U.J.M., Vol. 27 (1994), 10-22; Math. Rev. Author index 1996.
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; P.U.J.M., Vol. XXX, (1997).
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 Applied Mathematics Letters, Vol. 9, No. 2 (1996), 71-73; Math. Rev. Author index 1996.
135.: On the convergence of a Chebysheff-Halley-type method under Newton-Kantorovich hypotheses, Appl. Math. Letters, Vol. 6, No. 5 (1993), 71-74; Math. Rev. Author index 1996.
136.: On an application of a variant of the closed graph theorem and the secant method, Tamkang J. Math., Vol. 24, No. 3 (1993), 251-267; Math. Rev. 94m:65098, Rabindra Nath Sen.
137.: Newton-like methods in partially ordered Banach spaces, Approx. Theory and Its Applic., 9:1 (1993), 1-9; Math. Rev. 94f:47086, Mihai Turinici.
138.: Results on the Chebyshev method in Banach spaces, Proyecciones Revista, Vol. 12, No. 2 (1993), 119-128; Math. Rev. 94j:65078, A.M. Galperin (IL-BGUN; Be'er Sheva).
139.: On the convergence of an Euler-Chebysheff-type method under Newton-Kantorovich hypotheses, Pure Mathematics and Applications, Vol. 4, No. 3 (1993), 369-373; Math. Rev. 95g:65081, Tetsuro Yamamoto.
140.: A note on the Halley method in Banach spaces, Appl. Math. and Comp., 58 (1993), 215-224; Math. Rev. 94k:65082, Erich Bohl (Konstanz).
141.: On the solution of underdetermined systems of nonlinear equations in Euclidean spaces, Pure Mathematics and Applications, Vol. 4, No. 3 (1993), 199-209; Math. Rev. 95a:65089.
142.: On the a posteriori error bounds for a certain iteration under Zabrejko-Ngyen assumptions, Rev. Academia de Ciencias, Zaragoza, 48 (1993), 77-85; Math. Rev. 95b:65076.
143.: Newton-like methods in generalized Banach spaces, Functiones et Approximatio, XXII (1993), 107-114; Math. Rev. 95i:65088, Mihai Turinici.
144.: On S-order of convergence, Rev. Academia de Ciencias Zaragoza, 48 (1993), 69-76; Math. Rev. Author index 1994.
145.: A theorem on perturbed Newton-like methods in Banach spaces, Studia Scientiarum Mathematicarum Hungarica, 29 (1994), 295-305; Math. Rev. 95i:65089.
146.: Some notes on nonstationary multistep iteration processes, Acta Mathematica Hungarica, Vol. 64, 1 (1994), 59-64; Math. Rev. 94m:90098.
147.: Improved a posteriori error bounds for Zincenko's iteration, Intern. J. Comp. Math., Vol. 51 (1994), 51-54.
148.: The Jarratt method in a Banach space setting, J. Comp. Appl. Math., 51 (1994), 103-106; Math. Rev. 95c:65088.
149.: The midpoint method in Banach spaces and Ptak-error estimates, Appl. Math. and Computation, 62, 1 (1994), 1-15; Math. Rev. 95c:65087, Mihai Turinici.
150.: A convergence theorem for Newton-like methods under generalized Chen-Yamamoto-type assumptions, Appl. Math. and Comput., 61, 1 (1994), 25-37; Math. Rev. 65g:65082.
151.: On the convergence of some projection methods and inexact Newton-like iterations, Tamkang J. Math., Vol. 25, No. 4 (1994), 335-341; Math. Rev. 95m:65105, Mihai Turinici.
152.: On Newton's method and nonlinear operator equations, P.U.J.M., Vol. 27 (1994), 34-44; Math. Rev. Author index 1996.
153.: On the midpoint iterative method for solving nonlinear operator equations and applications to the solution of integral equations, Revue D'analyse Numerique et de Theorie de l'approximation, Tome 23, fasc. 2 (1994), 139-152; Math. Rev. 97j:65093.
154.: Parameter based algorithms for approximating local solutions of nonlinear complex equations, Proyecciones, Vol. 13, No. 1 (1994), 53-61; Math. Rev. 95f:65100.
155.: The Halley-Werner method in Banach spaces, 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).
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.
157.: Error bound representations of Chebysheff-Halley-type methods in Banach spaces, Rev. Academia de Ciencias Zaragoza, 49 (1994), 57-69; Math. Rev. 95j:65065.
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.
159.: On the discretization of Newton-like methods, Internat. J. Computer. Math., Vol. 52 (1994), 161-170.
160.: A local convergence theorem for the super-Halley method in a Banach space, Appl. Math. Lett., Vol. 7, No. 5 (1994), 49-52; Math. Rev. Author index 1996.
161.: A convergence analysis for a rational method with a parameter in Banach space, Pure Mathematics and Applications, 5, 1 (1994), 59-73; Math. Rev. 95j:65063.
162.: On sufficient conditions of the convergence and an optimality of error estimate for a high speed iterative algorithm for solving nonlinear algebraic systems, Chinese J. Math., Vol. 22, No. 4 (1994), 373-384; Math. Rev. 95i:65078, Xiaojun Chen.
163.: On the convergence of modified contractions, Journ. Comput. Appl. Math., 55, 2 (1994), 183-189; Math. Rev. 96a:65085.
164.: A multipoint Jarratt-Newton-type approximation algorithm for solving nonlinear operator equations in Banach spaces, Functiones et Aproximatio Commentarii Matematiki, XXIII (1994), 97-108; Math. Rev. 96c:65098.
165.: Convergence results for the super-Halley method using divided differences, Functiones et Approximatio Commentari Mathematici, XXIII (1994), 109-122; Math. Rev. 96d:6509.
166.: On the aposteriori error estimates for Stirling's method, Studia Scientiarum Mathematicarum Hungarica, 30, 3-4 (1995), 205-216; Math. Rev. 96g:65055, Otmar Scherzer (1-DE; Newark, DE).
167.: Sufficient conditions for the convergence of Newton-like methods under weak smoothness assumptions, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Conference on Computational and Applied Mathematics (1995), 1-13.
168.: On Stirlin's method, Tamkang J. Math., Vol. 27, No. 1 (1995).
169.: Stirling's method and fixed points of nonlinear operator equations in Banach space, 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).
170.: Error bounds for fast two-point Newton methods of order four, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Annual Conference on Computational and Applied Mathematics (1995), 14-18.
171.: Improved error bounds for fast two-point Newton methods of order three, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Annual Conference on Computational and Applied Mathematics (1995), 19-23; Rev. Academia de Ciencias, Zaragoza, 50 (1995), 15-19; Math. Rev. Author index 1996.
172.: Stirling's method in generalized Banach spaces, Annales Univ. Sci. Budapest. Sect. Comp., 15 (1995), 37-47; Math. Rev. 97m:47093 (George Isac).
173.: A unified approach for constructing fast two-step Newton-like methods, Monatshefte fur Mathematik, 119 (1995), 1-22; Math. Rev. 96a:65093, Otmar Scherzer (1-TXAM; College Station, TX).
174.: On the Secant method and the Ptak error estimates, Revue d'analyse Numerique et de theorie de l'approximation, 24, 1-2 (1995), 3-14; Math. Rev. 1998, pp. 58.
175.: An error analysis for the secant method under generalized Zabrejko-Nguen-type assumptions, Arabian Journal of Science and Engineering, 20:1 (1995), 197-206; Math. Rev. 96c:65100, A.M. Galperin (IL-BGUN; Be'er Sheva).
176.: Optimal-order parameter identification in solving nonlinear systems in a Banach space, Journal of Computational Mathematics, 13, 3 (1995), 267-280; Math. Rev. 96j:65070, A.A. Fonarev (Moscow).
177.: Nondifferentiable operator equations on Banach spaces with a convergence structure, Pure Mathematics and Applications, (PUMA), Vol. 6, 1 (1995), Math. Rev. 97h:47062.
178.: Perturbed Newton-like methods and nondifferentiable operator equations on Banach spaces with a convergence structure, (SWJPAM) Southwest Journal of Pure and Applied Mathematics, 1 (1995), 1-12; Math. Rev. 97k:65139, A.M. Galperin.
179.: Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure, (SWJPAM) Southwest Journal of Pure and Applied Mathematics, 1 (1995), 32-38; Math. Rev. 97k:65140.
180.: A study on the order of convergence of a rational iteration for solving quadratic equations in a Banach space, Rev. Academia de Ciencias, Zaragoza, 50 (1995), 35-40; Math. Rev. Author index 1996.
181.: On an application of a variant of the closed graph theorem to the solution of nonlinear equations, Pure Mathematics and Applications, (PUMA), 6, 4 (1995), 301-312; Math. Rev. 97b:47063, M.Z. Nashed.
182.: Results on Newton methods; Part I: A unified approach for constructing perturbed Newton-like methods in Banach space and their applications, Appl. Math. and Comp., 74, 2-3 (1996), 119-141; Math. Rev. 97b:65074, De Ren Wang.
183.: Results on Newton methods; Part II: Perturbed Newton-like methods in generalized Banach spaces, Appl. Math. and Comp., 74, 2-3 (1996), Math. Rev. 97b:65075, De Ren Wang.
184.: On the method of tangent hyperbolas, Journal of Approximation Theory and Its Applications, 12, 1 (1996), 78-96.
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.
186.: On the method of tangent parabolas, Functiones et Approximatio Commentarii Mathematici, XXIV (1996), 3-15; Math. Rev. 98a:65077.
187.: On an extension of the mesh-independence principle for operator equations in Banach space, Appl. Math. Lett., Vol. 9, No. 3 (1996), 1-7; Math. Rev. 97a:47108.
188.: An inverse-free Jarratt type approximation in a Banach space, Journal of Approximation Theory and Its Applications, 12, 1 (1996), 19-30; Math Rev. 1998, pp. 58.
189.: An error analysis for the Steffensen method under generalized Zabrejko-Nguen-type assumptions, Revue d'analyse Numerique et de theorie de l'approximation, 25, 1-2 (1996), 11-22.
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.
191.: Improved error bounds for an Euler-Chebysheff-type method, Pure Math. Appl. (PUMA), 7, 1-2 (1996), 41-51; Math. Rev. 97j:65097.
192.: On the convergence of perturbed Newton-like methods in Banach space and applications, Southwest J. Pure Appl. Math., 2 (1996), 34-41; Math Rev. 98b:65060.
193.: Sufficient conditions for the convergence of iterations to points of attraction in Banach spaces, Southwest J. Pure Appl. Math., 2 (1996), 42-47; Math. Rev. 98b:65061.
194.: Weak conditions for the convergence of iterations to solutions of equations on partially ordered topological spaces, Southwest J. Pure Appl. Math., 2 (1996), 48-54; Math Rev. 98b:65062.
195.: On the monotone convergence of implicit Newton-like methods, Southwest J. Pure Appl. Math., 2 (1996), 55-59; Math Rev. 98b:65063.
196.: A generalization of Edelstein's theorem on fixed points and applications, Southwest J. Pure Appl. Math., 2 (1996), 60-64; Math. Rev. 98a:65078.
197.: Generalized conditions for the convergence of inexact Newton methods on Banach spaces with a convergence structure and applications, Pure Mathematics and Applications (PUMA), 7, 3-4 (1996), 197-214; Math. Rev. Author index 1997.
198.: Error bounds for an almost fourth order method under generalized conditions, Rev. Academia de Ciencias, Zaragoza, 51 (1996), 19-26; Math. Rev. 98c:65091, Tetsuro Yamamoto.
199.: A simplified proof concerning the convergence and error bound for a rational cubic method in Banach spaces and applications to nonlinear integral equations, Rev. Academia de Ciercias, Zaragoza, 51 (1996), 47-55; Math. Rev. 98e:65074, Boro Döring.
200.: On the convergence of Chebysheff-Halley-type method using divided differences of order one, Rev. Academia de Ciercias, Zaragoza, 51 (1996), 27-45.
201.: On the convergence of two-step methods generated by point-to-point operators, Appl. Math. and Comput., 82, 1 (1997), 85-96; Math. Rev. 97m:65107, A.M. Galperin.
202.: Improved error bounds for Newton-like iterations under Chen-Yamamoto assumptions, Appl. Math. Lett., 10, 4 (1997), 97-100; Math. Rev. 1998, pp. 59.
203.: Inexact Newton methods and nondifferentiable operator equations on Banach spaces with a convergence structure, Approx. Th. Applic., 13, 3 (1997), 91-104.
204.: A mesh independence principle for inexact Newton-like methods and their discretizations under generalized Lipschitz conditions, Appl. Math. Comp., 87 (1997), 15-48; Math. Rev. 98d:65075, Asen L. Dontchev.
205.: On the super-Halley method using divided differences, Appl. Math. Lett., 10, 4 (1997), 91-95; Math. Rev. 1998, pp. 59.
206.: Chebysheff-Halley like methods in Banach spaces, Korean Journ. Comp. Appl. Math., Vol. 4, No. 1 (1997), 83-107; Math. Rev. 98a:47068, Tetsuro Yamamoto.
207.: Concerning the convergence of inexact Newton methods, J. Comp. Appl. Math., 79 (1997), 235-247; Math. Rev. 98c: 47077, P.P. Zabrejko.
208.: General ways of constructing accelerating Newton-like iterations on partially ordered topological spaces, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 18-22.
209.: Smoothness and perturbed Newton-like methods, Pure Mathematics and Applications (PUMA), 8, 1 (1997), 13-28; Math. Rev. 98h:65023.
210.: A mesh independence principle for operator equations and Steffensen-method, Korean J. Comp. Appl. Math., 4, 2 (1997), 263-280; Math. Rev. 98c:65092.
211.: Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications, Appl. Math. Lett., 10, 6 (1997), 21-28; Math. Rev. 1999, pp. 59.
212.: A new convergence theorem for Steffensen's method on Banach spaces and applications, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 23-29.
213.: A local convergence theorem for the inexact Newton method at singular points, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 30-36.
214.: Applications of a special representation of analytic functions, Southwest Journal of Pure and Applied Mathematics, 2 (December 1997), 43-47.
215.: On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations, IMA J. Num. Anal., Journal of the Institute of Mathematics and Its Applications, 18 (1997), 37-56.
216.: Results involving nondifferentiable equations on Banach spaces with a convergence structure and Newton methods, Rev. Academia de Ciencias, de Zarayoza, 52 (1997), 23-30.
217.: The asymptotic mesh independence principle for inexact Newton-Galerkin-like methods, PUMA, 8, 2-3-4, (1997), 169-194.
218.: The Halley method in Banach spaces and the Ptak error estimates, Rev. Academia de Ciencias, de Zaragoza, 52 (1997), 31-41.
219.: Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method, Southwest J. Pure Appl. Math., 1 (1998), 24-28.
220.: On the monotone convergence of an Euler-Chebysheff-type method in partially ordered topological spaces, Revue d'analyse Numerique et de theorie de l'approximation, 27, 1 (1998).
221.: Sufficient conditions for constructing methods faster than Newton's, Appl. Math. Comp, 93 (1998), 169-181.
222.: Error bounds for the Chebyshev method in Banach spaces, Bull. Inst. Acad. Sinica, 26, 4 (1998), 269-282.
223.: Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term, Revue d'analyse Numerique et de theorie de l'approximation, 27, 2 (1998).
224.: On the convergence of a certain class of iterative procedures under relaxed conditions with applications, J. Comp. Appl. Math., 94 (1998), 13-21.
225.: Improving the order and rates of convergence for the Super-Halley method in Banach spaces, Korean J. Comp. Appl. Math., 5, 2 (1998), 465-474.
226.: A new convergence theorem for the Jarratt method in Banach spaces, Computers and Mathematics with Applications, 36, 8 (1998), 13-18.
227.: On Newton's method under mild differentiability conditions and applications, Appl. Math. Comp., 102 (1999), 177-183.
228.: Improved error bounds for a Chebysheff-Halley-type method, Acta Math. Hungarica, 84, (3) (1999), 211-221.
230.: Convergence domains for some iterative processes in Banach spaces using outer and generalized inverses, J. Computational Analysis and Applications, Vol. 1, No. 1, (1999), 87-104.
231.: Concerning the convergence of a modified Newton-like method, Zeitschrift für analysis und ihre Anwendungen, Journal for Analysis and Applications, 18, (3) (1999), 1-8.
232.: A new convergence theorem for Newton-like methods in Banach space and applications, Comput. Appl. Math., 18, 3 (1999).
233.: A new convergence theorem for inexact Newton methods based on assumptions involving the second Fréchet-derivative, Computers and Mathematics with Applications, 37 (1999), 109-115.
234.: The Halley-Werner method in Banach spaces and the Ptak error estimates, Bulletin Hong-Kong Math. Soc. BHKMS, Vol. 2 (1999), 357-371.
235.: Concerning the radius of convergence of Newton's method and applications, Korean J. Comp. Appl. Math., Vol. 6, No. 3 (1999).
236.: Relations between forcing sequences and inexact-Newton-like iterates in Banach space, Intern. J. Comp. Math., 71 (1999), 235-246.
237.: On the applicability of two Newton methods for solving equations in Banach space, Korean J. Comp. Appl. Math., Vol. 6, No. 2 (1999), 267-275.
238.: Affine invariant local convergence theorems for inexact Newton-like methods, Korean J. Comp. Appl. Math., Vol. 6, No. 2 (1999), 291-304.
239.: A convergence analysis for Newton-like methods in Banach space under weak hypotheses and applications, Tamkang J. Math., Vol. 30, No. 4, 1999.
240.: An error analysis for the midpoint method, Tamkang J. Math., Vol. 30, No. 3, 1999.
241.: Newton methods on Banach spaces with a convergence structure and applications, Computers and Math. with Appl. Intern. J., Pergamon Press.
242.: Appproximating solutions of operator equations using modified contractions and applications, Studia Scientiarum Mathematicurum Hungarica, 35 (1999), 207-215.
243.: A fixed point proof of the convergence of extended Newton-like methods on Banach spaces and applications, Commun. Appl. Anal.
244.: 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, Commun. Appl. Anal.
245.: On the convergence of Steffensen-Galerkin methods, Atti del seminario Matematica e Fisico dell'universita di Modena.
246.: Convergence results for a fast iterative method in linear spaces, Taiwanese J. Math.
247.: Generalized conditions for the convergence of inexact Newton-like methods on Banach spaces with a convergence structure and applications, Korean J. Comp. Appl. Math.
248.: Accessibility of solutions of equations on Banach spaces by Newton-like methods and applications, Bulletin Inst. Math. Acad. Sinica.
249.: On the convergence of Newton's method for polynomial equations and applications in radiative transfer, Monatschefte für Mathematik, 27 (1999), 265-276.
250.: A convergence theorem for Newton's method under uniform-like continuity conditions on the second Fréchet-derivative, Atti del seminario Matematica e Fisico dell' universita di Mondena.
251.: A new convergence theorem for Stirling's method in Banach space, Atti del seminario Matematica e Fisico dell' universita di Modena.
252.: Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Letters.
253.: A generalization of Ostrowski's theorem on fixed points, Appl. Math. Letters.
254.: Choosing the forcing sequences for inexact Newton methods in Banach space, Comput. Appl. Math., 19, 1 (2000).
255.: A new Kantorovich-type theorem for Newton's method, Applicationes Mathematicae.
256.: A monotone convergence theorem for Newton-like methods using divided differences of order two, Southwest J. Pure Appl. Math.
257.: Perturbed Steffensen-Aitken projection methods for solving equations with nondifferentiable operators, Mathematica-Revue.
258.: On an application of a Steffen-Aitken-type method to the approximation of implicit functions, Mathematica-Revue.
259.: On controlling the residuals for Steffensen-Aitken-like methods, Mathematica-Revue.
260.: On the convergence of Steffensen-Aitken-like methods using divided differences obtained recursively, Adv. Nonlinear Var. Inequal., 3 (2000).
261.: The Steffensen method in generalized Banach spaces, Mathematica-Revue.
262.: Conditions for the convergence of perturbed Steffensen methods on a Banach space with a convergence structure, Adv. Nonlinear Var. Inequal., 2 (2000).
263.: A new convergence theorem for the Steffensen method in Banach space and applications, Mathematica-Revue.
264.: Local and global convergence results for a class of Steffensen-Aitken-type methods, Adv. Nonlinear Var. Ineq., 3 (2000).
265.: The Chebyshev method in Banach spaces and the Ptak error estimates, Revue d'analyse Numerique et de theorie de l'approximation.
266.: An error analysis for Steffensen's method, Revue d'analyse Numerique et de theorie de l'approximation.
267.: A convergence theorem for Steffensen's method and the Ptak error estimates, Revue d'analyse Numerique et de theorie de l'approximation.
268.: On some iterative methods for solving nonlinear equations with a nondifferentiable term of order between 1.618 $&ldots;$ and 1.839 $&ldots;$ , Revue d'analyse Numerique et de theorie de l'approximation.
269.: Convergence theorems for Newton-like methods under generalized Newton-Kantorovich conditions, Revue d'analyse numerique et de theorie de l'approximation.
270.: On the local convergence of m-step Newton methods with applications on a vector supercomputer, Revue d'analyse Numerique et de theorie de l'approximation.
271.: On some general iterative methods for solving nonlinear operator equations containing a nondifferentiable term, Adv. Nonlinear Var. Inequal., 3 (2000).
272.: Relations between forcing sequences and inexact Newton iterates in Banach space, Computing.
273.: Concerning the monotone convergence of the method of tangent hyperbolas, Korean J. Comp. Appl. Math.

Submitted for Publication

274.: Perturbed Newton methods in generalized Banach spaces.
275.: A mesh independence principle for perturbed Newton-like methods and their discretizations.
276.: On the convergence of an Euler-Chebysheff-type method using divided differences of order one.
277.: On the convergence of disturbed Mewton-like methods in Banach space.
278.: A convergence theorem for Newton-like methods in Banach space under general weak assumptions and applications.
279.: On the monotone convergence of a Chebysheff-Halley-type method in partially ordered topological spaces.
280.: Error bounds for the Halley-Werner method in Banach spaces.
281.: Error bounds for the Halley method in Banach spaces.
282.: A unified approach for solving nonlinear operator equations and applications.
283.: Error bounds for the midpoint method in Banach spaces.
284.: Enlarging the region of convergence for Steffensen's method on Banach spaces.
285.: Extending the region of convergence for a certain class of modified iterative methods on Banach space and applications.
286.: Semilocal convergence results for Newton-like methods using Kantorovich quasi-majorant functions involving the first derivative.
287.: A new convergence theorem for the secant method in Banach space and applications.
288.: A new convergence theorem for the method of tangent parabolas in Banach space.
289.: A new convergence theorem for the method of tangent hyperbolas.
290.: Convergence theorems for some variants of Newton's method of order greater than two.
291.: Improving the rate of convergence of Newton-like methods in Banach space using twice Fréchet-differentiable operators and applications.
292.: On the solution of nonlinear equations under Holder continuity assumptions
293.: Improved error bounds for Newton's method under hypotheses on the second Fréchet-derivative.
294.: Accessibility of solutions of equations on Banach spaces by a Stirling-like method.

Under Preparation

295.: Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet-derivative.
296.: Local convergence of inexact Newton-like iterative methods and applications.
297.: A unifying semilocal convergence theorem for Newton-like methods in Banach space.
298.: The effect of rounding errors on Newton-like methods in Banach space under hypotheses on the second Fréchet-derivative.
299.: Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the second Fréchet-derivative.
300.: Semilocal convergence theorems for a certain class of iterative procedures using outer or generalized inverses.
301.: Local convergence theorems of Newton's method for nonlinear equations using outer or generalized inverses.
302.: A global convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative.
303.: Improving the order of convergence of Newton's method for a certain class of polynomial equations.
304.: Convergence results for nonlinear equations under generalized Hölder continuity assumptions.
305.: On the approximation of quadratic equations in Banach space using finite rank operators.

(J) Other

The following professors have requested papers:

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

(K) Seminars

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.

(L) Papers Presented as an Invited Speaker

1.: University of Berkeley, International Summer Institute on Nonlinear Functional Analysis and Applications (1983). Title: ``On a contraction theorem and applications".
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".
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).
4.: Mathematical Association of America, Oklahoma-Arkansas Section, Spring 1991. Title: ``Improved bounds for the zeros of polynomials".
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".
6.: CAM 92, Edmond, OK, March 27, 1992, University of Central Oklahoma. Title: ``On the secant method under weak assumptions".
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".
8.: As in (7). Title: ``Sufficient convergence conditions for iterations schemes modeled by point-to-set mappings".
9.: As in (7). Title: ``On a two-point Newton method in Banach spaces and the Ptak error estimates".
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".
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".
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.
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".
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".
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".
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".
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".
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.
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".
20.: Coloquium Seminars University of Memphis, March 12, 1999. Title: ``Recent Developments on Discretization Studies".

(M) Selected Lectures Presented

1.: University of Georgia, 1982-1984
2.: University of Iowa, 1984-1986
3.: State University of Iowa, 1985
4.: Northern University of Viginia, 1986, 1988
5.: New Mexico State University, 1986-1990
6.: University of Ohio, 1986
7.: University of Iowa, 1986, 1988
8.: University of New York, 1986-1988
9.: University of Texas at El Paso, 1987-1990
10.: University of Arizona, I.E.D., 1989, 1990
11.: Portland State University, 1990
12.: Cameron University, 1990
13.: University of Central Oklahoma, 1992, 1993, 1994, 1995, 1996
14.: University of Cyprus, Nicosia Cyprus, 1993

(N) Other Meetings Attended

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

5. TEACHING EXPERIENCE

(A) Courses Taught

Graduate

1.: Numerical Solutions of Ordinary Differential Equations, Partial Differential Equations, Integral Equations, Integral Differential Equations
2.: The Finite Difference and the Finite-Element Method for Ordinary Differential Equations and Partial Differential Equations
3.: Differential Equations
4.: Partial Differential Equations
5.: Special Topics in Functional Analysis, Numerical Functional Analysis, and Differential Equations
6.: Numerical Solution of Functional Equations
7.: Advanced Numerical Analysis
8.: Thesis in Mathematics
9.: Optimization

Undergraduate Courses

1.: Calculus Courses
2.: Differential Equations
3.: Numerical Analysis
4.: Linear Algebra
5.: Real Analysis
6.: History of Mathematics
7.: Geometry
8.: Statistics
9.: Abstract Algebra
10.: Independent Study in Mathematics
11.: Matrix Algebra
12.: Survey of Mathematics
13.: Intermediate Algebra
14.: College Algebra

(B) Teaching Effectiveness

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.

6. AWARDS, HONORS AND AFFILIATIONS

(A) Conference Chairman

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

(B) Outstanding Graduation Record

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.

A total of 88 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.

7. DEPARTMENTAL SERVICE

1.: Member of the graduate studies committee (N.M.S.U.)
2.: Member of the graduate faculty (N.M.S.U.)
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.
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.
5.: See also previous items.

8. UNIVERSITY SERVICE

1.: I have been participating in the Cameron Interscholastic Service.
2.: I have been serving some of the Cameron faculty as consultant.
3.: Dean's representative (N.M.S.U.).
4.: See also previous items.

9. STUDENT SERVICE

1.: I have been participating in many of our student activities including Mathematics, Pi Mu Epsilon and CS Club activities.
2.: See also previous items.

10. COMMUNITY SERVICE

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

11. BRIEF DESCRIPTION OF SOME OF THE BOOKS AS LISTED IN 4(H)

1. The Theory and Applications of Iteration Methods

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 $x =f(x)$ , 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.

2. The Theory and Application of Abstract Polynomial Equations

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:

(a): Numerical methods for approximating distinct solutions of quadratic $(n =2)$ (in Chapters 1 and 2) and polynomial equations $(n ≥2)$ (in Chapter 3) are given;
(b): Results on global existence theorems not related with contractions are provided;
(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.

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.

3. A Survey of Efficient Numerical Methods and Applications

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

$F(x) =0 (E)$

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 )(n≥0), (N)

notation (S) denotes Secant method

$x$ _{n +1} =x_n - [x_n ,x_{n -1}]^-1 F(x_n )(n≥0), (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 )(n≥0). (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, Fréchet derivatives, and the relationship between them is being investigated.

Several unpublished results have also been added demonstrating how to select divided differences, Fréchet 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.,

$[x,y] ≤[u,v] for x≤u and y≤v.$

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 Fréchet-derivative $F'$ of $F$ of the form

$| F' (x) -F'(y)| ≤L| x-y| , or | F'(x) -F'(y)|≤
K(r)| x-y|$

or more recently by us

| F'(x +h)-F' (x)| ≤A(r,| h| )

for all

x,y

in a certain ball centered at a fixed point

x

₀, of radius

R>0

with

0
≤r≤R

and

| h| ≤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(x₀)|. 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

(1≤p <&inf;)

and

L

_&inf;.

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, Fréchet 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:

(a): Refined proofs using the same techniques are given;
(b): Different techniques have been applied;
(c): New techniques have been used;
(d): New results have been discovered.

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.

12. BRIEF DESCRIPTION OF PAPERS AS LISTED IN 4(I)

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 Fréchet derivative of the nonlinear operator involved be Fréchet-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 Hölder 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 perturbed 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.

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