Fixed Point Theory for Lipschitzian-type Mappings with Applications

  • Authors
  • D. R. Sahu
  • Donal O'Regan
  • Ravi P. Agarwal
Part of the Topological Fixed Point Theory and Its Applications book series (TFPT, volume 6)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 1-47
  3. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 49-125
  4. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 127-174
  5. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 175-209
  6. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 211-278
  7. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 279-313
  8. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 315-331
  9. Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 333-348
  10. Back Matter
    Pages 1-20

About this book

Introduction

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis.

This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields.

This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Keywords

Convexity Fixed-Point Theory Operator theory Smooth function banach spaces convergence theory fixed point theory functional analysis iterative processes problem of existence

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-75818-3
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-75817-6
  • Online ISBN 978-0-387-75818-3