A system of additive functional equations in complex Banach algebras

Abstract

In this article, we solve the system of additive functional equations: 2f(x+y)−g(x)=g(y),g(x+y)−2f(y−x)=4f(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 ff-hom-ders in Banach algebras.

Keywords

• additive mapping
• f-hom-der
• fixed point method
• hyers-ulam stability
• system of additive functional equations
• 47b47
• 17b40
• 39b72
• 47h10