SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP

Abstract

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation

f (x + y)^m = g(x)h(y),

where f,g,h : G → R are unknown mappings and m is a fixed positive integer. Here G is an Abelian group (G,+), and R the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. Gavruta’s result in 1994 and G. H. Kim’s results in 2011.