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| Author | : Bernardo Lafuerza Guillen |
| Publisher | : World Scientific |
| Total Pages | : 233 |
| Release | : 2014-08-01 |
| Genre | : Mathematics |
| ISBN | : 1783264705 |
Download Probabilistic Normed Spaces Book in PDF, ePub and Kindle
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: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.
| Author | : Bernardo Lafuerza Guillén |
| Publisher | : |
| Total Pages | : 220 |
| Release | : 2014 |
| Genre | : Mathematics |
| ISBN | : 9781783264681 |
Download Probabilistic Normed Spaces Book in PDF, ePub and Kindle
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.
| Author | : B. Schweizer |
| Publisher | : Courier Corporation |
| Total Pages | : 354 |
| Release | : 2011-10-14 |
| Genre | : Mathematics |
| ISBN | : 0486143759 |
Download Probabilistic Metric Spaces Book in PDF, ePub and Kindle
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.
| Author | : Bernardo Lafuerza Guillén |
| Publisher | : |
| Total Pages | : 233 |
| Release | : 2014-09-09 |
| Genre | : MATHEMATICS |
| ISBN | : 9781783264698 |
Download Probabilistic Normed Spaces Book in PDF, ePub and Kindle
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
| Author | : Dimitrios Drossos |
| Publisher | : |
| Total Pages | : 72 |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
Download Properties of Probabilistic Metric and Normed Spaces Book in PDF, ePub and Kindle
| Author | : K.P. Hart |
| Publisher | : Elsevier |
| Total Pages | : 537 |
| Release | : 2003-11-18 |
| Genre | : Mathematics |
| ISBN | : 0080530869 |
Download Encyclopedia of General Topology Book in PDF, ePub and Kindle
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
| Author | : O. Hadzic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 279 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401715602 |
Download Fixed Point Theory in Probabilistic Metric Spaces Book in PDF, ePub and Kindle
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.
| Author | : Shih-sen Chang |
| Publisher | : Nova Publishers |
| Total Pages | : 358 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9781560729808 |
Download Nonlinear Operator Theory in Probablistic Metric Spaces Book in PDF, ePub and Kindle
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.
| Author | : Jorgen Hoffmann-Jorgensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 422 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461202531 |
Download Probability in Banach Spaces, 9 Book in PDF, ePub and Kindle
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.
| Author | : Roman Vershynin |
| Publisher | : Cambridge University Press |
| Total Pages | : 299 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 1108415199 |
Download High-Dimensional Probability Book in PDF, ePub and Kindle
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
