Handbook of Metric Fixed Point Theory

  • William A. Kirk
  • Brailey Sims

Table of contents

  1. Front Matter
    Pages i-xiii
  2. W. A. Kirk
    Pages 1-34
  3. Brailey Sims
    Pages 35-48
  4. Kazimierz Goebel, W. A. Kirk
    Pages 49-91
  5. M. A. Khamsi, B. Sims
    Pages 177-199
  6. Jesús Garcia-Falset, Antonio Jiménez-Melado, Enrique Llorens-Fuster
    Pages 201-238
  7. T. Domínguez, M. A. Japón, G. López
    Pages 239-268
  8. P. N. Dowling, C. J. Lennard, B. Turett
    Pages 269-297
  9. Wieslawa Kaczor, Małgorzata Koter-Mórgowska
    Pages 323-337
  10. R. Espínola, M. A. Khamsi
    Pages 391-435
  11. Tadeusz Kuczumow, Simeon Reich, David Shoikhet
    Pages 437-515
  12. Anthony To-Ming Lau, Wataru Takahashi
    Pages 517-555
  13. Simeon Reich, Alexander J. Zaslavski
    Pages 557-575

About this book

Introduction

Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces.
Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts.
The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide 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.

Keywords

banach spaces compactness fixed point theory mathematical analysis metric space stability

Editors and affiliations

  • William A. Kirk
    • 1
  • Brailey Sims
    • 2
  1. 1.Department of MathematicsThe University of IowaIowa CityUSA
  2. 2.School of Mathematical and Physical SciencesThe University of NewcastleNewcastleAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1748-9
  • Copyright Information Springer Science+Business Media B.V. 2001
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5733-4
  • Online ISBN 978-94-017-1748-9
  • About this book