Topics In Metric Fixed Point Theory

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Topics In Metric Fixed Point Theory

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Author : Kazimierz Goebel
language : en
Publisher: Cambridge University Press
Release Date : 1990

Topics In Metric Fixed Point Theory written by Kazimierz Goebel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.

Metric Fixed Point Theory

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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-01-04

Metric Fixed Point Theory written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.

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.

Topics In Fixed Point Theory

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Author : Saleh Almezel
language : en
Publisher:
Release Date : 2013-11-30

Topics In Fixed Point Theory written by Saleh Almezel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-30 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.

Measures Of Noncompactness In Metric Fixed Point Theory

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Author : José María Ayerbe Toledano
language : en
Publisher: Springer Science & Business Media
Release Date : 1997

Measures Of Noncompactness In Metric Fixed Point Theory written by José María Ayerbe Toledano 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 1997 with Mathematics categories.

This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations. This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area. Most of the results presented here were obtained by the authors over the last ten years and have not previously appeared in any other textbook.

Fixed Point Theory In Probabilistic Metric Spaces

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Author : O. Hadzic
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30

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 2001-11-30 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.

Fixed Point Theory For Lipschitzian Type Mappings With Applications

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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12

Fixed Point Theory For Lipschitzian Type Mappings With Applications written by Ravi P. Agarwal 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 2009-06-12 with Mathematics categories.

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields. This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Handbook Of Metric Fixed Point Theory

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Author : William Kirk
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-30

Handbook Of Metric Fixed Point Theory written by William 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 2001-06-30 with Mathematics categories.

Preface. 1. Contraction Mappings and Extensions; W.A. Kirk. 2. Examples of Fixed Point Free Mappings; B. Sims. 3. Classical Theory of Nonexpansive Mappings; K. Goebel, W.A. Kirk. 4. Geometrical Background of Metric Fixed Point Theory; S. Prus. 5. Some Moduli and Constants Related to Metric Fixed Point Theory; E.L. Fuster. 6. Ultra-Methods in Metric Fixed Point Theory; M.A. Khamsi, B. Sims. 7. Stability of the Fixed Point Property for Nonexpansive Mappings; J. Garcia-Falset, A. Jiménez-Melado, E. Llorens-Fuster. 8. Metric Fixed Point Results Concerning Measures of Noncompactness; T. Dominguez, M.A. JapÃ3n, G. LÃ3pez. 9. Renormings of l1 and c0 and Fixed Point Properties; P.N. Dowling, C.J. Lennard, B. Turett. 10. Nonexpansive Mappings: Boundary/Inwardness Conditions and Local Theory; W.A. Kirk, C.H. Morales. 11. Rotative Mappings and Mappings with Constant Displacement; W. Kaczor, M. Koter-MÃ3rgowska. 12. Geometric Properties Related to Fixed Point Theory in Some Banach Function Lattices; S. Chen, Y. Cui, H. Hudzik, B. Sims. 13. Introduction to Hyperconvex Spaces; R. Espinola, M.A. Khamsi. 14. Fixed Points of Holomorphic Mappings: A Metric Approach; T. Kuczumow, S. Reich, D. Shoikhet. 15. Fixed Point and Non-Linear Ergodic Theorems for Semigroups of Non-Linear Mappings; A. To-Ming Lau, W. Takahashi. 16. Generic Aspects of Metric Fixed Point Theory; S. Reich, A.J. Zaslavski. 17. Metric Environment of the Topological Fixed Point Theorms; K. Goebel. 18. Order-Theoretic Aspects of Metric Fixed Point Theory; J. Jachymski. 19. Fixed Point and Related Theorems for Set-Valued Mappings; G.X.-Z. Yuan. Index.

Metric Structures And Fixed Point Theory

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Author : Dhananjay Gopal
language : en
Publisher: CRC Press
Release Date : 2021-04-08

Metric Structures And Fixed Point Theory written by Dhananjay Gopal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-08 with Mathematics categories.

It is an indisputable argument that the formulation of metrics (by Fréchet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach’s fixed point theorem. Because the underlying space of this theorem is a metric space, the theory that developed following its publication is known as metric fixed point theory. It is well known that metric fixed point theory provides essential tools for solving problems arising in various branches of mathematics and other sciences such as split feasibility problems, variational inequality problems, non-linear optimization problems, equilibrium problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations are closely related to fixed point theory. For this reason, many people over the past seventy years have tried to generalize the definition of metric space and corresponding fixed point theory. This trend still continues. A few questions lying at the heart of the theory remain open and there are many unanswered questions regarding the limits to which the theory may be extended. Metric Structures and Fixed Point Theory provides an extensive understanding and the latest updates on the subject. The book not only shows diversified aspects of popular generalizations of metric spaces such as symmetric, b-metric, w-distance, G-metric, modular metric, probabilistic metric, fuzzy metric, graphical metric and corresponding fixed point theory but also motivates work on existing open problems on the subject. Each of the nine chapters—contributed by various authors—contains an Introduction section which summarizes the material needed to read the chapter independently of the others and contains the necessary background, several examples, and comprehensive literature to comprehend the concepts presented therein. This is helpful for those who want to pursue their research career in metric fixed point theory and its related areas. Features Explores the latest research and developments in fixed point theory on the most popular generalizations of metric spaces Description of various generalizations of metric spaces Very new topics on fixed point theory in graphical and modular metric spaces Enriched with examples and open problems This book serves as a reference for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed points. It may also be used as a text book for postgraduate and research students who are trying to derive future research scope in this area.

Fixed Point Theorems And Applications

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Author : Vittorino Pata
language : en
Publisher: Springer Nature
Release Date : 2019-09-22

Fixed Point Theorems And Applications written by Vittorino Pata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-22 with Mathematics categories.

This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.