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Fixed Point Theory and Its Applications
Edited by: R. F. Brown

Contemporary Mathematics
1988; 268 pp; softcover
Volume: 72
Reprint/Revision History:
reprinted 1989
ISBN-10: 0-8218-5080-6
ISBN-13: 978-0-8218-5080-0
List Price: US$47
Member Price: US$37.60
Order Code: CONM/72
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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.

Table of Contents

  • V. Akis -- Quasi-retractions and the fixed point property
  • J. Baillon -- Nonexpansive mapping and hyperconvex spaces
  • J. Baillon and N. Rallis -- Not too many fixed points
  • R. Brown -- Nielsen fixed point theory and parametrized differential equations
  • P. Fitzpatrick and J. Pejsachowicz -- The fundamental group of the space of linear Fredholm operators and the global analysis of semilinear equations
  • D. Goncalves -- Braid groups and Wecken pairs
  • D. Gottlieb -- A de Moivre-like formula for fixed point theory
  • M. Grossinho -- Some existence results of nonselfadjoint problems at resonance
  • R. Guenther and J. Lee -- Topological transversality and differential equations
  • C. Hagopian -- Fixed points of tree-like continua
  • G. Isac -- Fixed point theory, coincidence equations on convex cones and complementarity problem
  • B. Jiang -- A characterization of fixed point classes
  • A. Kartsatos and M. Parrott -- Using fixed point theory to find the weak solution of an abstract functional differential equation
  • M. Kelly -- Fixed points through homotopies
  • P. Omari, G. Villari, and F. Zanolin -- A survey of recent applications of fixed point theory to the Lienard equation
  • J. Pak -- On the fibered Jiang spaces
  • S. Park -- Fixed point theorems on compact convex sets in topological vector spaces
  • J. Pejsachowicz -- \(K\)-theoretic methods in bifurcation theory
  • C. Prieto -- Fix-theory of diagrams
  • S. Reich -- Fixed point theory in the Hilbert ball
  • B. Rhoades -- Contractive definitions and continuity
  • R. Sine -- Remarks on a paper of Horn
  • F. Wille -- On Ljusternik-Schnirelmann theory and degree theory
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