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Nonstandard Methods in Fixed Point Theory

A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic r...

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Bibliographic Details
Main Authors: Aksoy, Asuman G., Khamsi, Mohamed A. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1990, 1990
Edition:1st ed. 1990
Series:Universitext
Subjects:
Mathematical Analysis
Analysis
Analysis (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Schauder Bases
  • 1
  • I. Filters
  • II. Limits over Filters
  • III.Nets
  • 2
  • I. The Set-Theoretic Ultraproduct
  • II. The Banach Space Ultraproduct
  • III. Finite Representability
  • IV. Super-(M)-Properties and Banach-Saks Properties
  • V. The Ultraproduct of Mappings
  • VI. Tzirelson and James Banach Spaces
  • 3
  • I. An Introduction to Fixed Point Theory
  • II. Basic Definitions and Results
  • III. Basic Results in Ultraproduct Language
  • IV. Some Fixed Point Theorems
  • V. Maurey’s Theorems
  • VI. An Application of Ultranets

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