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 (ϕ(X)) = φ(X)f (X)+ψ(X) and the stability in the sense of Ger for the functional equation of the form f (ϕ(X))= φ(X)f (X), where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers–Ulam–Rassias, Gˇavruta, and Ger for some well-known equations such as the gamma, beta, and G-function type’s equations.  2004 Elsevier Inc. All rights reserved