On Fixed Points In Uniform Spaces With Applications To Probabilistic Metric Spaces
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On Fixed Points In Uniform Spaces With Applications To Probabilistic Metric Spaces
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Author : Seppo Heikkilä
language : en
Publisher:
Release Date : 1978
On Fixed Points In Uniform Spaces With Applications To Probabilistic Metric Spaces written by Seppo Heikkilä and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Topology categories.
Fixed Point Theory In Probabilistic Metric Spaces
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Author : O. Hadzic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fixed Point Theory In Probabilistic Metric Spaces written by O. Hadzic 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 2013-06-29 with Mathematics categories.
Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
On Nonsymmetric Topological And Probabilistic Structures
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2006
On Nonsymmetric Topological And Probabilistic Structures written by Yeol Je Cho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In this book, generally speaking, some properties of bitopological spaces generated by certain non-symmetric functions are studied. These functions, called "probabilistic quasi-pseudo-metrics" and "fuzzy quasi-pseudo-metrics", are generalisations of classical quasi-pseudo metrics. For the sake of completeness as well as for convenience and easy comparison, most of the introductory paragraphs are mainly devoted to fundamental notions and results from the classical -- deterministic or symmetric -- theory.
Handbook Of Metric Fixed Point Theory
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Author : W.A. Kirk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Handbook Of Metric Fixed Point Theory written by W.A. Kirk 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 2013-04-17 with Mathematics categories.
Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide 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.
Modern Topics In Metrical Fixed Point Theory
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Author : Mihai Turinici
language : en
Publisher: World Scientific
Release Date : 2025-02-20
Modern Topics In Metrical Fixed Point Theory written by Mihai Turinici and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Mathematics categories.
Metrical Fixed Point Theory, originating from the 1922 Banach Fixed Point Theorem, is one of the most dynamic areas within Operator Equations Theory. This book aims to discuss the foundational aspects of this theory, focusing on questions of existence, uniqueness, and approximation in operator equations — whether explicit or implicit, anticipative or non-anticipative — across standard, ordered, and relational metric spaces. Key themes include implicit methods for analyzing metrical contractions, factorial techniques for reducing coincidence point problems to standard fixed point ones, homotopical fixed point results in gauge spaces with ordered metric space parameters, and constant class reduction of PPF-dependent fixed point results.The book is structured into four chapters. Chapter 1 provides an overview of essential preliminary concepts. Chapter 2 delves into various contraction classes within bi-relational, local Branciari, and ordered metric spaces. Chapter 3 applies maximal techniques to address the discussed questions, and Chapter 4 explores additional topics, including contractive-type conditions derived from self and non-self maps. Through this structure, the book offers a comprehensive view of the core aspects and applications of Metrical Fixed Point Theory.
Fixed Point Theory And Applications Proceedings Of The Second International Conference
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Author : Kok Keong Tan
language : en
Publisher: World Scientific
Release Date : 1992-08-08
Fixed Point Theory And Applications Proceedings Of The Second International Conference written by Kok Keong Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-08 with categories.
This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.
Scientiae Mathematicae Japonicae
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Author :
language : en
Publisher:
Release Date : 2001
Scientiae Mathematicae Japonicae written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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
Probabilistic Metric Spaces
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Author : B. Schweizer
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Probabilistic Metric Spaces written by B. Schweizer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
Bulletin Of The Institute Of Mathematics Academia Sinica
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Author : Zhong yang yan jiu yuan. Shu xue yan jiu suo
language : en
Publisher:
Release Date : 1994
Bulletin Of The Institute Of Mathematics Academia Sinica written by Zhong yang yan jiu yuan. Shu xue yan jiu suo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.