Nonstandard Methods In Fixed Point Theory
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Nonstandard Methods In Fixed Point Theory
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Author : Asuman G. Aksoy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonstandard Methods In Fixed Point Theory written by Asuman G. Aksoy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Nonstandard Methods In Fixed Point Theory
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Author : Asuman Gèuven Aksoy
language : en
Publisher:
Release Date :
Nonstandard Methods In Fixed Point Theory written by Asuman Gèuven Aksoy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Fixed point theory categories.
Nonstandard Methods In Functional Analysis
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Author : Siu-Ah Ng
language : en
Publisher: World Scientific
Release Date : 2010
Nonstandard Methods In Functional Analysis written by Siu-Ah Ng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz'' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg''s invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.
Nonstandard Methods In Fixed Point Theory
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Author : Asuman G Aksoy
language : en
Publisher:
Release Date : 1990-08-06
Nonstandard Methods In Fixed Point Theory written by Asuman G Aksoy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-06 with categories.
An Introduction To Metric Spaces And Fixed Point Theory
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Author : Mohamed A. Khamsi
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
An Introduction To Metric Spaces And Fixed Point Theory written by Mohamed A. Khamsi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
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.
Fixed Point Theory
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Author : Andrzej Granas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fixed Point Theory written by Andrzej Granas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non linear functional analysis, emphasizing developments related to the Leray Schauder theory. Using for the most part geometric methods, our study cen ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre supposes some familiarity with more advanced parts of algebraic topology. The "Miscellaneous Results and Examples", given in the form of exer cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The "Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.
Topics In Fixed Point Theory
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Author : Saleh Almezel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-23
Topics In Fixed Point Theory written by Saleh Almezel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Mathematics categories.
The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.
Fixed Point Theory And Graph Theory
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Author : Monther Alfuraidan
language : en
Publisher: Academic Press
Release Date : 2016-06-20
Fixed Point Theory And Graph Theory written by Monther Alfuraidan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. - Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments - Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach - Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications
Fixed Point Theory In Modular Function Spaces
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Author : Mohamed A. Khamsi
language : en
Publisher: Birkhäuser
Release Date : 2015-03-24
Fixed Point Theory In Modular Function Spaces written by Mohamed A. Khamsi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.
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.
Topological Fixed Point Theory In Suitable Banach Algebras With Applications
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Author : Aref Jeribi
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
Topological Fixed Point Theory In Suitable Banach Algebras With Applications written by Aref Jeribi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs. Its scope extends to a broad range of equations, encompassing nonlinear biological models as well as two-dimensional boundary value problems associated with burgeoning cell populations and functional systems of differential and integral inclusions. The book systematically introduces the principles of topological fixed-point theory, offering insights into various classes of both single-valued and multi-valued maps. The overarching goal is to disseminate key techniques and outcomes derived from fixed-point theory, with a specific emphasis on its application to both single-valued and multi-valued mappings within the framework of Banach algebras.