Restrict The Stability Of Functional Equations On The Domain

We investigated the Hyers-Ulam-Rassias stability of functional equation on restricted domains in this paper.The first chapter using general method to prove the Hyers-Ulam-Rassias stability for the multi-Cauchy functional equation on a restricted domain; Chapter 2 proves the stability for the multi-quadratic functional equation on a restricted domain; Chapter 3 mainly using general method to prove the Hyers-Ulam-Rassias stability for the Jensen-quadratic functional equation on a restricted domain; Chapter 4 proves the Hyers-Ulam-Rassias stability for the functional equation f(ax+by)= af(x)+bf(y) on restricted domains.