Fixed Point Theory and Its Applications: Proceedings of a Conference Held at the International Congress of Mathematicians, August 4-6, 1986

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Fixed point theory touches on many areas of mathematics, such as general topology, algebraic topology, nonlinear functional analysis, and ordinary and partial differential equations and serves as a useful tool in applied mathematics. This book represents the proceedings of an informal three-day seminar held during the International Congress of Mathematicians in Berkeley in 1986. Bringing together topologists and analysts concerned with the study of fixed points of continuous functions, the seminar provided a forum for presentation of recent developments in several different areas. The topics covered include both topological fixed point theory from both the algebraic and geometric viewpoints, the fixed point theory of nonlinear operators on normed linear spaces and its applications, and the study of solutions of ordinary and partial differential equations by fixed point theory methods. Because the papers range from broad expositions to specialized research papers, the book provides readers with a good overview of the subject as well as a more detailed look at some specialized recent advances.
 

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Contents

Quasiretractions and the fixed point property
1
Non expansive mapping and hyperconvex spaces
11
Not too many fixed points
21
Axisymmetric vortex motions with swirl
27
Nielsen fixed point theory and parametrized differential equations
33
The fundamental group of the space of linear Fredholm operators and the global analysis of semilinear equations
47
Braid groups and Wecken pairs
89
A de Moivre like formula for fixed point theory
99
Using fixed point theory to find the weak solution of an abstract functional differential equation
161
Fixed points through homotopies
167
A survey of recent applications of fixed point theory to the Lienard equation
171
On the fibered Jiang spaces
179
Fixed point theorems on compact convex sets intopological vector spaces
183
Ktheoretic methods in bifurcation theory
193
Fixtheory of diagrams
207
Fixed point theory in the Hilbert ball
225

Some existence results for nonselfadjoint problems at resonance
107
Topological transversality and differential equations
121
Fixed points of treelike continua
131
Fixed point theory coincidence equations on convex cones and complementarity problem
139
A characterization of fixed point classes
157
Contractive definitions and continuity
233
Remarks on a paper of Horn
247
On LjusternikSchnirelmann theory and degree theory
253
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