On a type of exponential functional equation and its superstability in the sense of Ger

Abstract

In this paper, we deal with a type exponential functional equation as follows $$f(xy)=f(x)^{g(y)},$$ where $f$ and $g$ are two real valued functions on a commutative semigroup. Our aim of this paper is to proved that the above functional equation in the sense of Ger is superstable.