# APPROXIMATE GENERALIZED EXPONENTIAL FUNCTIONS

• Lee, Eun-Hwi (Department of Matematics Jeonju University)
• Accepted : 2009.09.15
• Published : 2009.09.25
• 50 1

#### Abstract

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

#### Keywords

and phrases Exponential functional equation;Stability of functional equation;Superstability

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