On the stability of functional equations and a problem of Ulam

In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of fun ctional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research a re presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equ ations in Banach spaces and complementarity theory.