Probabilistic Metric Spaces
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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.
Nonlinear Operator Theory In Probablistic Metric Spaces
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Author : Shih-sen Chang
language : en
Publisher: Nova Publishers
Release Date : 2001
Nonlinear Operator Theory In Probablistic Metric Spaces written by Shih-sen Chang and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The purpose of this book is to give a comprehensive introduction to the study of non-linear operator theory in probabilistic metric spaces. This book is introduced as a survey of the latest and new results on the following topics: Basic theory of probabilistic metric spaces; Fixed point theorems for single-valued and multi-valued mappings in probabilistic metric spaces; Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces; Coincidence point theorems, minimisation and fixed degree theorems in probabilistic metric spaces; Probabilistic contractors, accretive mappings and topological degree in probabilistic normed spaces; Nonlinear semigroups and differential equations in probabilistic metric spaces; KKM theorems, minimax theorems and variational inequalities.
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.
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.
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.
Probabilistic Metric Spaces And Nonlinear Operator Theory
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Author : Shih-sen Chang
language : en
Publisher:
Release Date : 1994
Probabilistic Metric Spaces And Nonlinear Operator Theory written by Shih-sen Chang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Metric spaces categories.
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.
Fixed Point Theory In Probabilistic Metric Spaces
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Author : O. Hadzic
language : en
Publisher:
Release Date : 2014-01-15
Fixed Point Theory In Probabilistic Metric Spaces written by O. Hadzic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Probability Measures On Metric Spaces
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Author : K. R. Parthasarathy
language : en
Publisher: Academic Press
Release Date : 2014-07-03
Probability Measures On Metric Spaces written by K. R. Parthasarathy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.
Common Fixed Point Theorem In Probabilistic G Metric Space Menger
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Author : Samira Jalili Nargesi
language : en
Publisher: Eliva Press
Release Date : 2022-08-23
Common Fixed Point Theorem In Probabilistic G Metric Space Menger written by Samira Jalili Nargesi and has been published by Eliva Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with categories.
In this book, I first introduce the concepts of t-norm, distance distribution function and triangle function and then by using of these concepts, I introduce probabilistic metric space and Menger probabilistic generalized metric space. In the other section, by introducing the concepts of compatibility, weak compatible, property (E . A) and property G^* -(E . A) in a Menger probabilistic generalized metric space I show some fixed point theorems.