Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 1–5 Submitted: February 3, 1996. Published: July 8, 1996.

PREDICTIVE DISTRIBUTION FOR POLYTOMOUS LOGISTIC MODELS

WITH NONLINEAR LINK FUNCTIONS

M.A. Tabatabai and K.P. Singh

Abstract. This article is concerned with predictive distribution for polytomous logistic models with nonlinear link functions. Within a Bayesian framework, an approximation of the predictive distribution for determining probabilities is presented. We describe this method using nonlinear link functions. The generalized linear link function is simply a special case of nonlinear models. All of the generalized logistic models require nonlinear estimation procedures to evaluate maximum likelihood estimates.

(1991) A.M.S. Subject Classification Codes. 34.

Key Words and Phrases. polytomous logistic model,link function,predictive distribution

Cameron University, Lawton, Oklahoma E-Mail Address: mohammat@cameron.edu University of Alabama, Birmingham, Alabama \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 6–10 Submitted: March 1, 1996. Published: July 29, 1996.

A COMMON FIXED POINT THEOREM IN COMPLETE METRIC SPACES

R.A.RASHWAN AND A.M.SADEEK

Abstract. In this note we establish a common fixed point theorem in complete metric space s which generalizes some results in [2].

(1991) A.M.S. Subject Classification Codes. 47H10.

Key Words and Phrases. Common fixed points, complete metric spaces-generalized contractive conditions.

Department of Mathematics, Faculty of Science, Assiut University, Assiut, EGYPT

E-mail Address: assiut@frcu.enu.eg

\begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 11–28 Submitted: April 11, 1996. Published: August 5, 1996.

SET-THEORETICAL PROPERTIES OF EXTREME COMBINATORIAL PROBLEMS

Anatoly D. Plotnikov

Abstract. Concepts of constructive combinatorial problem and, in particular, of extreme combinatorial problem (ECP) are defined. It is announced a sequential principle of construction of the constructive combinatorial problems’ solution. This principle leads to necessity to consider ECP as system of independence with weighted elements. Auxiliary sets, which are connected to the solution of optimization problem, are defined. Concept of a normal form of the ECP is introduced. It is established that representation of a problem in normal form in some cases permits essentially to simplify an initial problem. It is introduced concepts of dual and self-dual problems. Two classes of combinatorial optimization problems, which are discerned by method of search of the admissible solution, are considered. Concept of the canonical form the ECP is introduced. It is shown that the problem in canonical form – new problem which is equivalent to initial, i.e. all optimum solutions of a problem in canonical form are the optimum solutions of an initial problem as well. The fulfilled researches in some cases simplify the search of the optimization problem solution.

(1991) A.M.S. Subject Classification Codes.

Key Words and Phrases. extreme combinatorial problem, auxiliary sets,normal form, canonical form, optimum solutions

Department of Applied Mathematics and Computing systems Vinnitsa State Technical University E-mail Address: aplot@cec.vstu.vinnica.ua \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 29–33 Submitted: April 11, 1995. Published: September 9, 1996.

COMMON FIXED POINTS BY ISHIKAWA

ITERATES IN METRIC LINEAR SPACES

R.A.RASHWAN

Abstract. In this paper we obtain a common fixed point theorem for Ishikawa iterates of tw o self-mappings on a metric linear space under various contractive conditions.

(1991) A.M.S. Subject Classification Codes. 47H10.

Key Words and Phrases. Metric linear space, F - norm, Contractive mappings, Ishikawa iterates, Common fixed point.

Mathematics Department, Faculty of Science, Assiut University, Assuit, EGYPT

E-mail Address: assiut@frcu.enu.eg

\begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 34–41 Submitted: June 17, 1996. Published: September 9, 1996.

ON THE CONVERGENCE OF PERTURBED NEWTON-LIKE

METHODS IN BANACH SPACE AND APPLICATIONS

Ioannis K. Argyros

Abstract. In this study we use disturbed Newton-like methods to approximate a locally unique solution of a nonlinear equation containing a nondifferentiable term. We choose the linear operators to be inverted at every step of the computation of the Newton iterates to be associated not only with the differentiable part of the equation as it has happened so far but also with the nondifferentiable part. This way the upper error bounds on the distances are smaller than before.

(1991) A.M.S. Subject Classification Codes. 65J15, 65B05, 65L50, 47H17, 49D15.

Key Words and Phrases. Disturbed Newton-like methods, Banach space, Mysovskii theorem, divided difference of order one, Fréchet-derivative.

Cameron University, Lawton, Oklahoma E-mail Address: ioannisa@cameron.edu \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 42–47 Submitted: June 19, 1995. Published: September 25, 1996.

SUFFICIENT CONDITIONS FOR THE CONVERGENCE OF

ITERATIONS TO POINTS OF ATTRACTION IN BANACH SPACE

Ioannis K. Argyros

Abstract. In this study we provide weak sufficient conditions for the convergence of iterations to points of attraction in Banach space. Our results are used to show existence and uniqueness of solutions of nonlinear equations. We complete our study with an example that shows that our convergence results apply where earlier ones do not.

(1991) A.M.S. Subject Classification Codes. 65J15, 47H17, 49D15.

Key Words and Phrases. Banach space, points of attraction, nonlinear equation.

Cameron University, Lawton, Oklahoma

E-mail Address: ioannisa@cameron.edu

\begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 48–54 Submitted: August 11, 1996. Published: October 15, 1996.

WEAK CONDITIONS FOR THE CONVERGENCE

OF ITERATIONS TO SOLUTIONS OF EQUATIONS

ON PARTIALLY ORDERED TOPOLOGICAL SPACES

Ioannis K. Argyros

Abstract. We provide sufficient conditions for the monotone convergence of Newton-like methods to solutions of nonlinear operator equations on partially ordered topological spaces. We assume conditions weaker than standard Lipschitz-like conditions to produce two iterations, one increasing and one decreasing, that enclose and converge to a solution of an equation. Finally examples are given to show that our results apply where previous ones fail.

(1991) A.M.S. Subject Classification Codes. 65J15, 47H17, 49D15.

Key Words and Phrases. Partially ordered topological space, monotone convergence, fixed point, Newton-like methods.

Cameron University, Lawton, Oklahoma E-mail Address: ioannisa@cameron.edu \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 55–59 Submitted: September 23, 1996. Published: November 7, 1996.

ON THE MONOTONE CONVERGENCE

OF IMPLICIT NEWTON-LIKE METHODS

Ioannis K. Argyros

Abstract. In this study, we examine the convergence of implicit Newton-like methods to a solution of a nonlinear equation on a partially ordered topological space. We generate two sequences, one increasing and one decreasing that enclose a solution of the nonlinear equation. Finally, we provide an example that shows that our method converges whereas the standard explicit Newton-like method does not.

(1991) A.M.S. Subject Classification Codes. 65J15, 65B05, 47H17, 49D15.

Key Words and Phrases. Newton-like method, monotone convergence, partially ordered topological space.

Cameron University, Lawton, Oklahoma E-mail Address: ioannisa@cameron.edu \begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University

Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 60–64 Submitted: October 17, 1996. Published: December 9, 1996.

A GENERALIZATION OF EDELSTEIN’S THEOREM

ON FIXED POINTS AND APPLICATIONS

Ioannis K. Argyros

Abstract. In this study, we approximate fixed points of nonlinear equations on topological vector spaces using implicit methods. A new Edelstein type theorem on fixed points is proved. The advantage of these methods is that they can be used to solve equations that usual explicit methods cannot.

(1991) A.M.S. Subject Classification Codes. 65J15, 47H17, 49D15.

Key Words and Phrases. Implicit methods, fixed point, topological vector space, normed space.

Cameron University, Lawton, Oklahoma

E-mail Address: ioannisa@cameron.edu

\begin{matrix}c \\ ◯ \end{matrix}1996 Cameron University