Fixed Point Theory in Modular Function Spaces

  • Mohamed A. Khamsi
  • Wojciech M. Kozlowski

Table of contents

  1. Front Matter
    Pages i-x
  2. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 1-4
  3. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 5-46
  4. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 47-77
  5. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 79-109
  6. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 111-169
  7. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 171-184
  8. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 185-218
  9. Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 219-234
  10. Back Matter
    Pages 235-245

About this book

Introduction

This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable.

 

The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.​

Keywords

Fixed Point Iterative Processes Metric Fixed Point Theory Modular Function Space Modular Metric Space Orlicz Space

Authors and affiliations

  • Mohamed A. Khamsi
    • 1
  • Wojciech M. Kozlowski
    • 2
  1. 1.Department of Mathematical SciencesThe University of Texas at El PasoEl PasoUSA
  2. 2.University of New South WalesSydneyAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-14051-3
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-14050-6
  • Online ISBN 978-3-319-14051-3
  • About this book