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Fixed Point Theory in Modular Function Spaces

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Fixed Point Theory in Modular Function Spaces/ by Mohamed A. Khamsi, Wojciech M. Kozlowski.
Author:	Khamsi, Mohamed A.
other author:	Kozlowski, Wojciech M.
Description:	X, 245 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Operator theory. -
Online resource:	https://doi.org/10.1007/978-3-319-14051-3
ISBN:	9783319140513

Fixed Point Theory in Modular Function Spaces
Khamsi, Mohamed A.

Fixed Point Theory in Modular Function Spaces[electronic resource] /by Mohamed A. Khamsi, Wojciech M. Kozlowski. - 1st ed. 2015. - X, 245 p.online resource.

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.

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.

ISBN: 9783319140513

Standard No.: 10.1007/978-3-319-14051-3doiSubjects--Topical Terms:

527910
Operator theory.

LC Class. No.: QA329-329.9

Dewey Class. No.: 515.724

Fixed Point Theory in Modular Function Spaces
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505 0 $a 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.
520 $a 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.
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