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: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.
Probabilistic Normed Spaces
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Author : Bernardo Lafuerza Guillén
language : en
Publisher:
Release Date : 2014
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 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.
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.
Probabilistic Metric Spaces
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Author : B. Schweizer
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
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 2011-11-30 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.
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.
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
Stability Of Functional Equations In Random Normed Spaces
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Author : Yeol Je Cho
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-27
Stability Of Functional Equations In Random Normed Spaces written by Yeol Je Cho 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 2013-08-27 with Mathematics categories.
This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.
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.
Industry 5 0 And Paradigm Shift Emerging Challenges
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Author : Namit Gupta
language : en
Publisher: Allied Publishers
Release Date : 2023-01-23
Industry 5 0 And Paradigm Shift Emerging Challenges written by Namit Gupta and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Technology & Engineering categories.
Industry 5.0 is the successor of the 'Industry 4.0' concept which employed high technology in the manufacturing industry. Industry 5.0 is a new idea that adds a human touch to the work of robots and smart machines. The basic idea of humans and machines working together is to increase efficiency and effectivity, like the 'Internet of things' (loT). It aims to merge the increasing cognitive computing abilities of the robots with the intelligence and resourcefulness of the humans. The progress of Industry 5.0 is inevitable. As the technology grows more each day, we find ways to make our work simpler. The development of such technologies to make the world more efficient requires its manufacturers, i.e., humans who collaborate with these machines and technologies. Humans are indispensable resources, as what a machine can do is limited. And with all these efficiencies we have come so far, there is no path leading us back. With adoption of new concepts comes a paradigm shift as development continues and we move from Industry 4.0 which speaks of the "future of production," its primary purpose continues to be achieving seamless connectivity between machines and IT systems for higher productivity and efficiencies across the value chain. Overall, it focuses mainly on traditional financial and operational KPIs. Whereas Industry 5.0 gives a human touch to the concept of 4.0 keeping in mind the well-being of the environment and society, making the machines and humans work together on a path of 'Green Future'. Industry 5.0 has the balance of both humans and technologies which benefits the ecosystem, with discovery of new energy sources and renewable resources, helping in a sustainable working environment. It can be used to reduce harmful residue caused due to manufacturing processes and recycle rare materials. Taking this theme, the multidisciplinary congress on "Industry 5.0 and Paradigm Shift: Emerging Challenges" will highlight research challenges and open issues that should be further developed to realize Industry 5.0.