Generalized Metric Spaces And Mappings

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Generalized Metric Spaces and Mappings

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Author : Shou Lin
Publisher : Springer
ISBN 13 : 9462392161
Total Pages : 341 pages
Book Rating : 4.4/5 (623 download)

Book Synopsis Generalized Metric Spaces and Mappings by : Shou Lin

Download or read book Generalized Metric Spaces and Mappings written by Shou Lin and published by Springer. This book was released on 2016-10-20 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.

Fixed Point Theory in Generalized Metric Spaces

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Author : Erdal Karapinar
Publisher : Springer Nature
ISBN 13 : 3031149696
Total Pages : 141 pages
Book Rating : 4.0/5 (311 download)

Book Synopsis Fixed Point Theory in Generalized Metric Spaces by : Erdal Karapinar

Download or read book Fixed Point Theory in Generalized Metric Spaces written by Erdal Karapinar and published by Springer Nature. This book was released on 2022-12-07 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.

Handbook of Set-Theoretic Topology

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Author : K. Kunen
Publisher : Elsevier
ISBN 13 : 148329515X
Total Pages : 1282 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Handbook of Set-Theoretic Topology by : K. Kunen

Download or read book Handbook of Set-Theoretic Topology written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Fixed Point Theory in Metric Spaces

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Author : Praveen Agarwal
Publisher : Springer
ISBN 13 : 9811329133
Total Pages : 173 pages
Book Rating : 4.8/5 (113 download)

Book Synopsis Fixed Point Theory in Metric Spaces by : Praveen Agarwal

Download or read book Fixed Point Theory in Metric Spaces written by Praveen Agarwal and published by Springer. This book was released on 2018-10-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials. The book is a valuable resource for a wide audience, including graduate students and researchers.

Metric Fixed Point Theory

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Author : Pradip Debnath
Publisher : Springer Nature
ISBN 13 : 9811648964
Total Pages : 356 pages
Book Rating : 4.8/5 (116 download)

Book Synopsis Metric Fixed Point Theory by : Pradip Debnath

Download or read book Metric Fixed Point Theory written by Pradip Debnath and published by Springer Nature. This book was released on 2022-01-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.

Handbook of Metric Fixed Point Theory

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Author : W.A. Kirk
Publisher : Springer Science & Business Media
ISBN 13 : 9401717486
Total Pages : 702 pages
Book Rating : 4.4/5 (17 download)

Book Synopsis Handbook of Metric Fixed Point Theory by : W.A. Kirk

Download or read book Handbook of Metric Fixed Point Theory written by W.A. Kirk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A New Structure for Generalized Metric Spaces

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Author : Zead Mustafa
Publisher :
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.:/5 (225 download)

Book Synopsis A New Structure for Generalized Metric Spaces by : Zead Mustafa

Download or read book A New Structure for Generalized Metric Spaces written by Zead Mustafa and published by . This book was released on 2005 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis and Applications

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Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Fixed Point Theory in Distance Spaces

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Author : William Kirk
Publisher : Springer
ISBN 13 : 3319109278
Total Pages : 176 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis Fixed Point Theory in Distance Spaces by : William Kirk

Download or read book Fixed Point Theory in Distance Spaces written by William Kirk and published by Springer. This book was released on 2014-10-23 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.

Iterated Contraction Mappings and Fixed Point Theorems in Metric Spaces

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Author : Frank Hynes
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (456 download)

Book Synopsis Iterated Contraction Mappings and Fixed Point Theorems in Metric Spaces by : Frank Hynes

Download or read book Iterated Contraction Mappings and Fixed Point Theorems in Metric Spaces written by Frank Hynes and published by . This book was released on 1972 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Analysis

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Author : Themistocles M Rassias
Publisher : World Scientific
ISBN 13 : 9814513652
Total Pages : 571 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Nonlinear Analysis by : Themistocles M Rassias

Download or read book Nonlinear Analysis written by Themistocles M Rassias and published by World Scientific. This book was released on 1988-01-01 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Fixed Point Theory and Nonlinear Problems (Th Rassias)Global Linearization Iterative Methods and Nonlinear Partial Differential Equations III (M Altman)On Generalized Power Series and Generalized Operational Calculus and Its Application (M Al-Bassam)Multiple Solutions to Parametrized Nonlinear Differential Systems from Nielsen Fixed Point Theory (R Brown)The topology of Ind-Affine Sets (P Cherenack)Almost Approximately Polynomial Functions (P Cholewa)Cohomology Classes and Foliated Manifolds (M Craioveanu & M Puta)Bifurcation and Nonlinear Instability in Applied Mathematics (L Debnath)The Stability of Weakly Additive Functional (H Drljevic)Index Theory for G-Bundle Pairs with Applications to Borsuk-Ulam Type Theorems for G-Sphere Bundles (E Fadell & S Husseini)Nonlinear Approximation and Moment Problem (J S Hwang & G D Lin)Periods in Equicontinuous Topological Dynamical Systems (A Iwanik et al.)Continuation Theorems for Semi-Linear Equations in Banach Spaces: A Survey (J Mawhin & K Rybakowski)On Contractifiable Self-Mappings (P Meyers)Normal Structures and Nonexpansive Mappings in Banach Spaces (J Nelson et al.): Survey on Uniqueness and Classification Theorems for Minimal Surfaces (Th Rassias)Contractive Definitions (B Rhoades)On KY Fan's Theorem and Its Applications (S Singh)Fixed Points of Amenable Semigroups of Differentiable Operators (P Soardi)Research Problems on Nonlinear Equations (Th Rassias) Readership: Mathematicians and applied scientists. Keywords:Nonlinear Analysis;Nonlinear Partial Differential Equations III;Polynomial Functions;Cohomology Classes;Foliated Manifolds;Topological Dynamical Systems;Minimal Surfaces;Differentiable Operators;Nonlinear Equations

An Introduction to Metric Spaces and Fixed Point Theory

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Author : Mohamed A. Khamsi
Publisher : John Wiley & Sons
ISBN 13 : 1118031326
Total Pages : 318 pages
Book Rating : 4.1/5 (18 download)

Book Synopsis An Introduction to Metric Spaces and Fixed Point Theory by : Mohamed A. Khamsi

Download or read book An Introduction to Metric Spaces and Fixed Point Theory written by Mohamed A. Khamsi and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Applications

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Author : Ravi P. Agarwal
Publisher : Cambridge University Press
ISBN 13 : 1139433792
Total Pages : 182 pages
Book Rating : 4.1/5 (394 download)

Book Synopsis Fixed Point Theory and Applications by : Ravi P. Agarwal

Download or read book Fixed Point Theory and Applications written by Ravi P. Agarwal and published by Cambridge University Press. This book was released on 2001-03-22 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Mathematical Analysis and Applications

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Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030313395
Total Pages : 694 pages
Book Rating : 4.0/5 (33 download)

Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

Fixed Point Theory in Modular Function Spaces

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Author : Mohamed A. Khamsi
Publisher : Birkhäuser
ISBN 13 : 3319140515
Total Pages : 251 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis Fixed Point Theory in Modular Function Spaces by : Mohamed A. Khamsi

Download or read book Fixed Point Theory in Modular Function Spaces written by Mohamed A. Khamsi and published by Birkhäuser. This book was released on 2015-03-24 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fixed Point Theory in Probabilistic Metric Spaces

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Author : O. Hadzic
Publisher : Springer Science & Business Media
ISBN 13 : 9401715602
Total Pages : 279 pages
Book Rating : 4.4/5 (17 download)

Book Synopsis Fixed Point Theory in Probabilistic Metric Spaces by : O. Hadzic

Download or read book Fixed Point Theory in Probabilistic Metric Spaces written by O. Hadzic and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inverse Images of Generalized Metric Spaces Under Closed Maps

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Author : John Marshall Atkins
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (971 download)

Book Synopsis Inverse Images of Generalized Metric Spaces Under Closed Maps by : John Marshall Atkins

Download or read book Inverse Images of Generalized Metric Spaces Under Closed Maps written by John Marshall Atkins and published by . This book was released on 1972 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: