HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON IN RINGS

Abstract

The study of stability problems for various functional equations originated from a famous talk given by Stanislaw M. Ulam in 1940 and from a solution to Ulam's question presented by Donald H. Hyers in the following year. During the last decades, 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 di®erence. This remarkable result of Rassias directed the concern of mathematicians towards the study of stability problems of functional equations.