Fixed Point Theory in Ordered Sets and Applications

From Differential and Integral Equations to Game Theory

  • Siegfried Carl
  • Seppo Heikkilä

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Siegfried Carl, Seppo Heikkilä
    Pages 1-21
  3. Siegfried Carl, Seppo Heikkilä
    Pages 23-55
  4. Siegfried Carl, Seppo Heikkilä
    Pages 57-129
  5. Siegfried Carl, Seppo Heikkilä
    Pages 131-178
  6. Siegfried Carl, Seppo Heikkilä
    Pages 179-195
  7. Siegfried Carl, Seppo Heikkilä
    Pages 197-259
  8. Siegfried Carl, Seppo Heikkilä
    Pages 261-315
  9. Siegfried Carl, Seppo Heikkilä
    Pages 317-399
  10. Siegfried Carl, Seppo Heikkilä
    Pages 401-457
  11. Back Matter
    Pages 459-477

About this book

Introduction

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. It begins with a discussion of some simple examples of the order-theoretic fixed point results along with simple applications from each of the diverse fields. The fixed point theory is then developed and preliminary results on multi-valued variational inequalities regarding the topological and order-theoretical structure of solution sets are covered. This is followed by more advanced material which demonstrates the power of the developed fixed point theory. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given in an appendix chapter to make the book self-contained.

Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Keywords

Inequalities Integration theory Nonlinear analysis Order-theoretic

Authors and affiliations

  • Siegfried Carl
    • 1
  • Seppo Heikkilä
    • 2
  1. 1.Halle-Wittenberg, Institut für MathematikMartin-Luther-UniversitätHalleGermany
  2. 2., Department of Mathematical SciencesUniversity of OuluOuluFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7585-0
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7584-3
  • Online ISBN 978-1-4419-7585-0
  • About this book