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.
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 : 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.
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.
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.
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.
Probabilistic Metric Spaces
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Author : Berthold Schweizer
language : de
Publisher:
Release Date : 1983
Probabilistic Metric Spaces written by Berthold Schweizer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Boolean Valued Probabilistic Metric Spaces
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Author : Mickey Charles Holsey
language : en
Publisher:
Release Date : 1989
Boolean Valued Probabilistic Metric Spaces written by Mickey Charles Holsey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
In this paper the Boolean valued method is used to develop a theory closely resembling the theory of probabilistic metric spaces. In this development the complete Boolean algebra used must have the form of the quotient algebra of some atomless probability space ($Omega,{cal A},P$) modulo its class of null sets. In this setting the real numbers in the Boolean valued model, $Vsp{cal B}$, correspond to random variables with domain $Omega$, and the sets which act as binary operations on $Re$ in the model correspond to binary operations on the class of random variables with domain $Omega$. The next step is to generalize the theory of metric spaces by requiring the triangle inequality be satisfied for some generalized addition $oplus$ (i.e. some commutative, associative, nondecreasing binary operation on $Resp+$ which has 0 as identity). If the generalized addition is continuous then the generalized metric space has a natural topology on it which satisfies the same general properties that metric topologies satisfy. A Boolean valued probabilistic metric space is a triple ($tilde S,{cal D},{cal G}$) which corresponds to some triple ($S,d,oplus$) in $Vsp{cal B}$ which acts as a generalized metric space in the nonstandard model. Thus $tilde S$ is a subset of $Vsp{cal B},{cal D}$ is a function which maps ordered pairs of elements of $tilde S$ to a.e. nonnegative random variables, and ${cal G}$ is a binary operation on the class of a.e. nonnegative random variables. The topology on the generalized metric space in $Vsp{cal B}$ corresponds to a topology on $tilde S$ which is uniform. There are a large number of probabilistic metric spaces which can be isomorphically injected into some Boolean valued probabilistic metric space. This mapping is generally not a surjection due to the richer structure of the Boolean valued probabilistic metric space. There are also probabilistic metric spaces which cannot be isomorphically injected into any Boolean valued probabilistic metric space. This paper leads to several interesting lines of inquiry. One of these is whether all uniform topological spaces may be obtained from some generalized metric space by the Boolean valued method and another is what systems in the sciences can Boolean valued probabilistic metric spaces be used to model.
Encyclopedia Of General Topology
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Author : K.P. Hart
language : en
Publisher: Elsevier
Release Date : 2003-11-18
Encyclopedia Of General Topology written by K.P. Hart and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-18 with Mathematics categories.
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms