Communications of the
Korean Mathematical Society CKMS

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))=\phi(X)f(X)$, where $X$ lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and G{\v a}vruta for many other equations such as the gamma, beta, Schr\"{o}der, iterative, and $G$-function type's equations.

Keywords: functional equation, gamma, beta and G-function, Hyers-Ulam stability, Hyers-Ulam-Rassias stability

MSC numbers: 39B52, 39B72, 39B82