# Fixed Point Theory and Its Applications

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*R. F. Brown*

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.

# Table of Contents

## Fixed Point Theory and Its Applications

- Table of Contents vii8 free
- Preface ix10 free
- Quasi-retractions and the fixed point property 112 free
- Non expansive mapping and hyperconvex spaces 1122
- Not too many fixed points 2132
- Axisymmetric vortex motions with swirl 2738
- Nielsen fixed point theory and parametrized differential equations 3344
- The fundamental group of the space of linear Fredholm operators and the global analysis of semilinear equations 4758
- Braid groups and Wecken pairs 89100
- A de Moivre like formula for fixed point theory 99110
- Some existence results for nonselfadjoint problems at resonance 107118
- Topological transversality and differential equations 121132
- Fixed points of tree-like continua 131142
- Fixed point theory, coincidence equations on convex cones and complementarity problem 139150
- A characterization of fixed point classes 157168
- Using fixed point theory to find the weak solution of an abstract functional differential equation 161172
- Fixed points through homotopies 167178
- A survey of recent applications of fixed point theory to the Lienard equation 171182
- On the fibered Jiang spaces 179190
- Fixed point theorems on compact convex sets intopological vector spaces 183194
- K-theoretic methods in bifurcation theory 193204
- Fix-theory of diagrams 207218
- Fixed point theory in the Hilbert ball 225236
- Contractive definitions and continuity 233244
- Remarks on a paper of Horn 247258
- On Ljusternik-Schnirelmann theory and degree theory 253264