Topics in Fixed Point Theory, 1st Edition

  • Published By:
  • ISBN-10: 3319015869
  • ISBN-13: 9783319015866
  • DDC: 515.7248
  • Grade Level Range: College Freshman - College Senior
  • 304 Pages | eBook
  • Original Copyright 2014 | Published/Released June 2014
  • This publication's content originally published in print form: 2014

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The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland's variational principle.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Introduction to Metric Fixed Point Theory.
2: Banach Contraction Principle and Its Generalizations.
3: Ekeland's Variational Principle and Its Extensions with Applications.
4: Fixed Point Theory in Hyperconvex Metric Spaces.
5: An Introduction to Fixed Point Theory in Modular Function Spaces.
6: Fixed Point Theory in Ordered Sets from the Metric Point of View.
7: Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps.
8: Some Iterative Methods for Fixed Point Problems.