On the Hyers-Ulam-Rassias stability of functional equations in n-variables

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form f(phi(X)) = phi (X) f (X) + psi (X) and the stability in the sense of Ger for the functional equation of the form f (phi(X)) = phi (X) f (X), where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers-Ulam-Rassias, Gavruta, and Ger for some well-known equations such as the gamma, beta, and G-function type's equations. (C) 2004 Elsevier Inc. All rights reserved.