A system of additive functional equations in complex Banach algebras

Abstract

In this article, we solve the system of additive functional equations: 2 f (x + y) - g (x) = g (y), g (x + y) - 2 f (y - x) = 4 f (x) \left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}2f\left(x+y)-g\left(x)=g(y),\\ g\left(x+y)-2f(y-x)=4f\left(x)\end{array}\right. and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f f -hom-ders in Banach algebras.