**Contemporary Mathematics**

Volume: 21;
1983;
218 pp;
Softcover

MSC: Primary 47;
Secondary 54

Print ISBN: 978-0-8218-5023-7

Product Code: CONM/21

List Price: $40.00

Individual Member Price: $32.00

**Electronic ISBN: 978-0-8218-7607-7
Product Code: CONM/21.E**

List Price: $40.00

Individual Member Price: $32.00

# Topological Methods in Nonlinear Functional Analysis

Share this page *Edited by *
*S. P. Singh; S. Thomeier; B. Watson*

This volume contains the proceedings of the special session on Fixed Point Theory and Applications held during the Summer Meeting of the American Mathematical Society at the University of Toronto, August 21–26, 1982. The theory of contractors and contractor directions is developed and used to obtain the existence theory under rather weak conditions. Theorems on the existence of fixed points of nonexpansive mappings and the convergence of the sequence of iterates of nonexpansive and quasi-nonexpansive mappings are given. Degree of mapping and its generalizations are given in detail. A class of eventually condensing mappings is studied and multivalued condensing mappings with multiple fixed points are also given. Topological fixed points, including the study of the Nielsen number of a selfmap on a compact surface, extensions of a well-known result of Krasnosel‴ski&ibreve;'s Compression of a Cone Theorem, are given. Also, fixed points, antipodal points, and coincidences of multifunctions are discussed. Several results with applications in the field of partial differential equations are given. Application of fixed point theory in the area of Approximation Theory is also illustrated.

#### Table of Contents

# Table of Contents

## Topological Methods in Nonlinear Functional Analysis

- Contents v6 free
- Introduction vi7 free
- Contractors and Fixed Points 18 free
- The Degree of Mapping, and its Generalizations 1522
- Multiple Fixed Points of Compact Maps on Wedgelike ANRS in Banach Spaces 4148
- The Nielsen Numbers on Surfaces 5966
- A Good Class of Eventually Condensing Maps 99106
- Iteration Process for Nonexpansive Mappings 115122
- The Best Approximation of Bivariate Functions by Separable Functions 125132
- Positive Solutions of Operator Equations in the Nondifferentiable Case 137144
- On Fixed Points of Nonexpansive Mappings 147154
- Large Oscillations of Forced Nonlinear Differential Equations 151158
- Fixed Points and Sequences of Iterates in Locally Convex Spaces 159166
- Fixed Point Theorems and Jung Constant in Banach Spaces 167174
- Some Results on Multiple Positive Fixed Points of Multivalued Condensing Maps 171178
- Some Problems and Results in Fixed Point Theory 179186
- Contractive Definitions Revisited 189196
- Fixed Points, Antipodal Points and Coincidences of n-Acyclic Multifunctions 207214
- A Coincidence Theorem for Topological Vector Spaces 213220
- Some Random Fixed Point Theorems 215222