Fixed Point Theory in Modular Function Spaces by Mohamed A. KhamsiFixed Point Theory in Modular Function Spaces by Mohamed A. Khamsi

Fixed Point Theory in Modular Function Spaces

byMohamed A. Khamsi, Wojciech M. Kozlowski

Hardcover | April 7, 2015

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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.
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. ...
Title:Fixed Point Theory in Modular Function SpacesFormat:HardcoverDimensions:245 pagesPublished:April 7, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319140507

ISBN - 13:9783319140506


Table of Contents

Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.