Mohamed A. Khamsi's Books

A Problem Book in Real Analysis

By: Asuman G. Aksoy,Mohamed A. Khamsi

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A Problem Book in Real Analysis

By: Asuman G. Aksoy,Mohamed A. Khamsi

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

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Page Count

257

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441912967

ISBN 13

9781441912961

Fixed Point Theory in Modular Function Spaces

By: Mohamed A. Khamsi,Wojciech M. Kozlowski

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Fixed Point Theory in Modular Function Spaces

By: Mohamed A. Khamsi,Wojciech M. Kozlowski

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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Page Count

251

Publisher

Birkhäuser

Published Date

ISBN 10

3319140515

ISBN 13

9783319140513

An Introduction to Metric Spaces and Fixed Point Theory

By: Mohamed A. Khamsi,William A. Kirk

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An Introduction to Metric Spaces and Fixed Point Theory

By: Mohamed A. Khamsi,William A. Kirk

Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.

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Page Count

318

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118031326

ISBN 13

9781118031322

Nonstandard Methods in Fixed Point Theory

By: Asuman G. Aksoy,Mohamed A. Khamsi

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Nonstandard Methods in Fixed Point Theory

By: Asuman G. Aksoy,Mohamed A. Khamsi

A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point theoretic results which follow. Set theoretic and Banach space ultraproducts constructions are studied in detail in the second part of the book, while the remainder of the book gives an introduction to the classical fixed point theory in addition to a discussion of normal structure. This is the first book which studies classical fixed point theory for non-expansive maps in the view of non-standard methods.

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Page Count

149

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461234441

ISBN 13

9781461234449

Book's by Mohamed A. Khamsi

A Problem Book in Real Analysis

A Problem Book in Real Analysis

Fixed Point Theory in Modular Function Spaces

Fixed Point Theory in Modular Function Spaces

An Introduction to Metric Spaces and Fixed Point Theory

An Introduction to Metric Spaces and Fixed Point Theory

Nonstandard Methods in Fixed Point Theory

Nonstandard Methods in Fixed Point Theory

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