Overview
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.
Full Product Details
Author: Yeol Je Cho ,
Themistocles M. Rassias ,
Reza Saadati
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 2013 ed.
Volume: 86
Dimensions:
Width: 15.50cm
, Height: 1.60cm
, Length: 23.50cm
Weight: 5.266kg
ISBN: 9781461484769
ISBN 10: 1461484766
Pages: 246
Publication Date: 27 August 2013
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
The first two chapters (of the book) nicely provide background of the theory of random normed spaces. The literature on the Cauchy, Jensen, quadratic and cubic functional equations is significant. The Cauchy and cubic equations are almost completely investigated in the book. ... The book could prove to be useful for graduate students who are interested in the Hyers-Ulam-Rassias stability of functional equations. -M. S. Moslehian, ZbMATH
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 Brzdek, 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)
