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- Presents results proved in detail with several outlines examples to make the presentation of the theory well understood by large audiences
- Discusses useful research to both pure and applied mathematicians who search for both new and old results
- Presents written results for scientists and engineers who are orienting their study in the language of interdisciplinary research?
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 86)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“The book should interest any professional mathematician whose research is connected with functional equations, especially their stability in random spaces; I also can recommend it for graduate students interested in the subject. It could serve as a complete and independent introduction to the field of stability of functional equations in random spaces and as an excellent source of references for further study.” (Janusz Brzdęk, SIAM Review, Vol. 57 (1), March, 2015)
“The book under review is essentially a collection of several recent papers related to the stability of functional equations in the framework of fuzzy and random normed spaces. … useful for graduate students who are interested in the Hyers-Ulam-Rassias stability of functional equations.” (Mohammad Sal Moslehian, zbMATH, Vol. 1281, 2014)
Authors and Affiliations
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Gyeongsang National University, Chinju, Korea, Republic of (South Korea)
Yeol Je Cho
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National Technical University of Athens, Athens, Greece
Themistocles M. Rassias
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Iran University of Science and Technology, Behshahr, Iran
Reza Saadati
Bibliographic Information
Book Title: Stability of Functional Equations in Random Normed Spaces
Authors: Yeol Je Cho, Themistocles M. Rassias, Reza Saadati
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-1-4614-8477-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-8476-9Published: 27 August 2013
Softcover ISBN: 978-1-4939-0110-4Published: 26 August 2015
eBook ISBN: 978-1-4614-8477-6Published: 27 August 2013
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: XIX, 246
Topics: Functional Analysis, Optimization, Partial Differential Equations