On the Stability of Functional Equations in $n$-variables and its applications
Commun. Korean Math. Soc. 2005 Vol. 20, No. 2, 321-338
Printed June 1, 2005
Gwang Hui Kim
Kangnam University
Abstract : 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
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