Probabilistic normed spaces
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 spac…
Read More ↓Title Statements
- Full title :Probabilistic normed spaces / Bernardo Lafuerza Guillen, Panackal Harikrishnan.
Summary
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-d.
Read More ↓Edition Statements
- Publication Date:©2014
Publication Statements
- Publisher(s):Imperial College Press
- Place of Publication:London
- Language:eng
- Publication Date:©2014
The Physical Object
- Description:1 online resource (233 pages)
Edition Identifiers
- ISBN:9781783264698, 1783264691
- oclc:ocn891387171
- LC Classification:QA322.2
- Dewey Decimal:515/.73
Table of Contents
9.1 Boundedness of Linear Operators9.2 Classes of Linear Operators; 9.3 Probabilistic Norms for Linear Operators; 9.4 Completeness Results; 9.5 Families of Linear Operators; 10. Stability of Some Functional Equations in PN Spaces; 10.1 Mouchtari-Serstnev Theorem; 10.2 Stability of a Functional Equation in PN Spaces; 10.3 The Additive Cauchy Functional Equation in RN Spaces: Stability; 10.4 Stability in the Quartic Functional Equationin RN Spaces; 10.4.1 The quartic functional equation in RN spaces: stability; 10.5 A Functional Equation in Menger PN Spaces
10.5.1 Probabilistic stability of the functional equation (10.5.1)11. Menger's 2-Probabilistic Normed Spaces; 11.1 Accretive Operators in 2-PN Spaces; 11.2 Convex Sets in 2-PN Spaces; 11.3 Compactness and Boundedness in 2-PN Spaces; 11.4 D-Boundedness in 2-PN Spaces; Bibliography; Index
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