# ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

KIM, GWANG-HUI

• Published : 2005.01.01
• 58 4

#### Abstract

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

#### Keywords

Functional equation;Hyers-Ulam stability;Hyers-Ulam­Rassias stability;G-function;double gamma function

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