Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis - ISBN:1441996362

Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis

Date: 23 May 2011, 04:23

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Preface
An intriguing and famous talk presented by Stanislaw M. Ulam in 1940 triggered the study of stability problems for various functional equations. In his talk, Ulam discussed a number of important unsolved mathematical problems. Among them, a question concerning the stability of homomorphisms seemed too abstract for anyone to reach any conclusion. In the following year, Donald H. Hyers was able to give a partial solution to Ulam’s question that was the ?rst signi?cant breakthrough and step toward more solutions in this area. Since then, a large number of papers have been published in connection with various generalizations of Ulam’s problem and Hyers’s theorem. In particular, Themistocles M. Rassias succeeded in extending the result of Hyers’s theorem by weakening the condition for the Cauchy difference. This remarkable result of Rassias led the concern of mathematicians toward the study of stability problems of functional equations.
Unfortunately, no books dealing with a comprehensive illustration of the fast developing ?eld of nonlinear analysis had been published for the mathematicians interested in this ?eld for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias published their book, Stability of Functional Equations in Several Variables,Birkh? auser, 1998.
This very book will complement the books of Hyers, Isac and Rassias and of Czerwik (Functional Equations and Inequalities in Several Variables,World Scienti?c, 2002) by presenting mainly the results applying to the Hyers–Ulam–Rassias stability. Many mathematicians have extensively investigated the subjects on the Hyers–Ulam–Rassias stability. This book covers and offers almost all classical results on the Hyers–Ulam–Rassias stability in an integrated and self-contained fashion.

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