Topological Methods in Nonlinear Functional Analysis, Volumes 1-2

Front Cover
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 Krasnoselskii'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.
 

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Contents

Contractors and Fixed Points
1
The Degree of Mapping and its Generalizations
15
Multiple Fixed Points of Compact Maps on Wedgelike ANRS in Banach Spaces
41
The Nielsen Numbers on Surfaces
59
A Good Class of Eventually Condensing Maps
99
Iteration Process for Nonexpansive Mappings
115
The Best Approximation of Bivariate Functions by Separable Functions
125
Positive Solutions of Operator Equations in the Nondifferentiable Case
137
Fixed Points and Sequences of Iterates in Locally Convex Spaces
159
Fixed Point Theorems and Jung Constant in Banach Spaces
167
Some Results on Multiple Positive Fixed Points of Multivalued Condensing Maps
171
Some Problems and Results in Fixed Point Theory
179
Contractive Definitions Revisited
189
Fixed Points Antipodal Points and Coincidences of nAcyclic Multifunctions
207
A Coincidence Theorem for Topological Vector Spaces
213
Some Random Fixed Point Theorems
215

On Fixed Points of Nonexpansive Mappings
147
Large Oscillations of Forced Nonlinear Differential Equations
151

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