Fixed Point Theory In Probabilistic Metric Spaces
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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 In Probabilistic Metric Spaces
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Author : Olga Hadžić
language : en
Publisher:
Release Date : 1995
Fixed Point Theory In Probabilistic Metric Spaces written by Olga Hadžić and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Fixed point theory categories.
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.
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 Theory And Applications
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2007-08
Fixed Point Theory And Applications 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 2007-08 with Mathematics categories.
This volume deals with new topics in the areas of fixed point theory, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.
Fixed Point Theory And Applications Volume 6
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2007
Fixed Point Theory And Applications Volume 6 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 2007 with Mathematics categories.
Fixed Point Theory & Applications
Probabilistic Metric Spaces
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Author : B. Schweizer
language : en
Publisher: Courier Corporation
Release Date : 2011-10-14
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 2011-10-14 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.
Triangular Norms
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Author : Erich Peter Klement
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Triangular Norms written by Erich Peter Klement 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 Philosophy categories.
The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.
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.
Fixed Point Theory
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Author : V.I. Istratescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Fixed Point Theory written by V.I. Istratescu 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.
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will find the final G. K. Chesterton, The Scandal of Father question. Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.