Superstability of a generalized exponential functional equation of Pexider type

Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 357-369 Printed September 1, 2008

Young Whan Lee Daejeon University

Abstract : We obtain the superstability of a generalized exponential functional equation $$ f(x+y) = E(x,y)g(x)f(y) $$ and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$ \left| \frac{f(x + y)}{E(x, y)g(x)f(y)} - 1 \right| \ \leq \varphi(x,y), $$ where $E(x,y)$ is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

Keywords : exponential functional equation, stability of functional equations, superstability of functional equations, Cauchy functional equation