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Fixed Point Theory in Modular Function Spaces

  • Book
  • © 2015

Overview

Authors:
  1. Mohamed A. Khamsi

    1. Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, USA

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  2. Wojciech M. Kozlowski

    1. University of New South Wales, Sydney, Australia

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    You can also search for this author in PubMed   Google Scholar

  • Presents state-of-the-art advancements in the field of modular function theory

  • Provides a self-contained overview of the topic

  • Includes open problems, extensive bibliographic references, and suggestions for further development

  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 1-4

  3. Fixed Point Theory in Metric Spaces: An Introduction

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 5-46

  4. Modular Function Spaces

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 47-77

  5. Geometry of Modular Function Spaces

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 79-109

  6. Fixed Point Existence Theorems in Modular Function Spaces

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 111-169

  7. Fixed Point Construction Processes

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 171-184

  8. Semigroups of Nonlinear Mappings in Modular Function Spaces

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 185-218

  9. Modular Metric Spaces

    • Mohamed A. Khamsi, Wojciech M. Kozlowski
    Pages 219-234

  10. Back Matter

    Pages 235-245
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Keywords

About this book

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.​

Reviews

“The book is essentially self-contained and it provides an outstanding resource for those interested in this line of research.” (María Angeles Japón Pineda, Mathematical Reviews, March, 2016)

“The book is devoted to a comprehensive treatment of what is currently known about the fixed point theory in modular function spaces. … the book will be useful for all mathematicians whose interests lie in nonlinear analysis, in particular, in the theory of function spaces and fixed point theory.” (Peter P. Zabreĭko, zbMATH 1318.47002, 2015)

Authors and Affiliations

  • Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, USA

    Mohamed A. Khamsi

  • University of New South Wales, Sydney, Australia

    Wojciech M. Kozlowski

About the authors

Mohamed Amine Khamsi, Ph.D. is a Professor in the Department of Mathematical Sciences at the University of Texas at El Paso, Texas, USA.  His research interests include functional analysis, fixed point theory, discrete dynamical systems, and logic programming. Dr. Khamsi received his Ph.D. at the University Paris VI in 1987.

Wojciech M. (Walter) Kozlowski, Ph.D. is a professor in the School of Mathematics and Statistics at the University of New South Wales in Sydney, Australia. His research interests include functional analysis, function spaces, fixed point theory, approximation theory and applications. He received his doctorate at the Jagiellonian University in Krakow in 1981. Dr. Kozlowski, a Fulbright Scholar at the California University of Technology in Pasadena in years 1986 - 1988, works also in a capacity of the business consultant for the telecommunications industry.

Bibliographic Information

  • Book Title: Fixed Point Theory in Modular Function Spaces

  • Authors: Mohamed A. Khamsi, Wojciech M. Kozlowski

  • DOI: https://doi.org/10.1007/978-3-319-14051-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-14050-6Published: 07 April 2015

  • Softcover ISBN: 978-3-319-34635-9Published: 05 October 2016

  • eBook ISBN: 978-3-319-14051-3Published: 24 March 2015

  • Edition Number: 1

  • Number of Pages: X, 245

  • Topics: Operator Theory, Functional Analysis

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