Probabilistic Metric Spaces

2011-10-14
 |  Mathematics
Probabilistic Metric Spaces

Author: B. Schweizer

Publisher: Courier Corporation

ISBN: 9780486143750

Category: Mathematics

Page: 354

View: 490

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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.

Fixed Point Theory in Probabilistic Metric Spaces

2013-06-29
 |  Mathematics
Fixed Point Theory in Probabilistic Metric Spaces

Author: O. Hadzic

Publisher: Springer Science & Business Media

ISBN: 9789401715607

Category: Mathematics

Page: 273

View: 904

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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.

Probabilistic Metric Spaces

2011-11-30
 |  Mathematics
Probabilistic Metric Spaces

Author: B. Schweizer

Publisher: Courier Corporation

ISBN: 9780486445144

Category: Mathematics

Page: 354

View: 343

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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

2001
 |  Metric spaces
Nonlinear Operator Theory in Probablistic Metric Spaces

Author: Shih-sen Chang

Publisher: Nova Publishers

ISBN: 1560729805

Category: Metric spaces

Page: 358

View: 490

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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 and Applications

2007-08
 |  Fixed point theory
Fixed Point Theory and Applications

Author: Yeol Je Cho

Publisher: Nova Publishers

ISBN: 1594548773

Category: Fixed point theory

Page: 216

View: 963

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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.

On Nonsymmetric Topological and Probabilistic Structures

2006
 |  Nonsymmetric matrices
On Nonsymmetric Topological and Probabilistic Structures

Author: Yeol Je Cho

Publisher: Nova Publishers

ISBN: 1594549176

Category: Nonsymmetric matrices

Page: 230

View: 565

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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.