Stability of Functional Equations in Random Normed Spaces
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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.
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
"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)