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Fixed Point Theory for Lipschitzian-type Mappings with Applications

  • Book
  • © 2009

Overview

Authors:
  1. D. R. Sahu
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  2. Donal O'Regan
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  3. Ravi P. Agarwal
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  • Presents many basic techniques and results in fixed point theory
  • Self-contained presentation
  • Good graduate text with exercises at the end of each chapter

Part of the book series: Topological Fixed Point Theory and Its Applications (TFPT, volume 6)

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-9
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  2. Fundamentals

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 1-47

  3. Convexity, Smoothness, and Duality Mappings

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 49-125

  4. Geometric Coefficients of Banach Spaces

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 127-174

  5. Existence Theorems in Metric Spaces

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 175-209

  6. Existence Theorems in Banach Spaces

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 211-278

  7. Approximation of Fixed Points

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 279-313

  8. Strong Convergence Theorems

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 315-331

  9. Applications of Fixed Point Theorems

    • Ravi P. Agarwal, Donal O’Regan, D.R. Sahu
    Pages 333-348

  10. Back Matter

    Pages 1-20
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Keywords

About this book

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.

Reviews

From the reviews: “The present book explains many of the basic techniques and … the classical results of fixed point theory, and normal structure properties. … Exercises are included in each chapter. As such, it is a self-contained book that can be used in a course for graduate students.” (Srinivasa Swaminathan, Zentralblatt MATH, Vol. 1176, 2010) “This book provides a presentation of fixed point theory for Lipschitzian type mappings in metric and Banach spaces. … An exercise section is included at the end of each chapter, containing interesting and well chosen material in order to cover topics complementing the main body of the text. … It is worthwhile to point out that a beginner in this area is certainly well served with this text … . A book including all … topics together for sure should be welcomed for graduate students.” (Enrique Llorens-Fuster, Mathematical Reviews, Issue 2010 e)

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