Probabilistic Normed Spaces
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Probabilistic Normed Spaces
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Author : Bernardo Lafuerza Guillen
language : en
Publisher: World Scientific
Release Date : 2014-08-01
Probabilistic Normed Spaces written by Bernardo Lafuerza Guillen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include: What are PN spaces?The topology of PN spacesProbabilistic norms and convergenceProducts and quotients of PN spacesD-boundedness and D-compactnessNormabilityInvariant and semi-invariant PN spacesLinear operatorsStability of some functional equations in PN spacesMenger's 2-probabilistic normed spaces The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. Contents:PreliminariesProbabilistic Normed SpacesThe Topology of PN SpacesProbabilistic Norms and ConvergenceProducts and Quotients of PN SpacesD-Boundedness and D-CompactnessNormabilityInvariant and Semi-Invariant PN SpacesLinear OperatorsStability of Some Functional Equations in PN SpacesMenger's 2-Probabilistic Normed Spaces Readership: Post graduate students and researchers in the field of Probabilistic Normed Spaces. Key Features:The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equationsDeals with all the developed ideas in PN spacesA good reference book for post graduate students and researchers in this field as it identifies the developments and open problems in PN spacesKeywords:Probabilistic Normed Spaces;Normability in PN Spaces;D-Boundedness;D-Compactness;Topology in PN Spaces;Linear Operators in PN Spaces;Menger's 2-Probabilistic Normed Spaces;Invariant and Semi-Invariant PN SpacesReviews: “This book provides a good opportunity for scholars and students to get familiar with the theory of PN spaces and to acquire the basic knowledge in this field.” Zentralblatt MATH
Probabilistic Normed Spaces
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Author : Bernardo Lafuerza Guillén
language : en
Publisher:
Release Date : 2014-09-09
Probabilistic Normed Spaces written by Bernardo Lafuerza Guillén and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-09 with MATHEMATICS categories.
This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include:: What are PN spaces?; The topology of PN spaces; Probabilistic norms and convergence; Products and quotients of PN spaces; D -boundedness and D -compactness; Normability; Invariant and semi-invariant PN spaces; Linear operators; Stability of some functional equations in PN spaces; Menger''s 2-probabilistic normed spaces . The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. Contents: Preliminaries; Probabilistic Normed Spaces; The Topology of PN Spaces; Probabilistic Norms and Convergence; Products and Quotients of PN Spaces; D -Boundedness and D -Compactness; Normability; Invariant and Semi-Invariant PN Spaces; Linear Operators; Stability of Some Functional Equations in PN Spaces; Menger''s 2-Probabilistic Normed Spaces. Readership: Post graduate students and researchers in the field of Probabilistic Normed Spaces. Key Features: The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations; Deals with all the developed ideas in PN spaces; A good reference book for post graduate students and researchers in this field as it identifies the developments and open problems in PN spaces
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.
Probability In Banach Spaces 9
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Author : Jorgen Hoffmann-Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability In Banach Spaces 9 written by Jorgen Hoffmann-Jorgensen 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 2012-12-06 with Mathematics categories.
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, even about familiar processes, by stripping away details, that in hindsight turn out to be extraneous. A good understanding about the disciplines involved in this field can be obtained from the recent book, Probability in Banach Spaces, Springer-Verlag, by M. Ledoux and M. Thlagrand. On page 5, of this book, there is a list of previous conferences in probability in Banach spaces, including the other eight international conferences. One can see that research in this field over the last twenty years has contributed significantly to knowledge in probability and has had important applications in many other branches of mathematics, most notably in statistics and functional analysis.
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: 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.
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
Probability In Banach Spaces 9
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Author : Jorgen Hoffmann-Jorgensen
language : en
Publisher: Birkhäuser
Release Date : 1994-08-01
Probability In Banach Spaces 9 written by Jorgen Hoffmann-Jorgensen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-01 with Mathematics categories.
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, even about familiar processes, by stripping away details, that in hindsight turn out to be extraneous. A good understanding about the disciplines involved in this field can be obtained from the recent book, Probability in Banach Spaces, Springer-Verlag, by M. Ledoux and M. Thlagrand. On page 5, of this book, there is a list of previous conferences in probability in Banach spaces, including the other eight international conferences. One can see that research in this field over the last twenty years has contributed significantly to knowledge in probability and has had important applications in many other branches of mathematics, most notably in statistics and functional analysis.
Probability In Banach Spaces
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Author : Michel Ledoux
language : en
Publisher: Springer
Release Date : 2011-07-08
Probability In Banach Spaces written by Michel Ledoux and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-08 with Mathematics categories.
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.