On approximate cubic homomorphisms

Abstract

In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of the system of functional equations $$f(xy)=f(x)f(y),.f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x),$$ on Banach algebras. Indeed we establish the superstability of above system by suitable control functions.

11 pages