Combined system of additive functional equations in Banach algebras

Abstract

In this study, we solve the system of additive functional equations: h(x+y)=h(x)+h(y),g(x+y)=f(x)+f(y),2fx+y2=g(x)+g(y),\left\{\begin{array}{l}h\left(x+y)=h\left(x)+h(y),\\ g\left(x+y)=f\left(x)+f(y),\\ 2f\left(\frac{x+y}{2}\right)=g\left(x)+g(y),\end{array}\right. and we investigate the stability of (homomorphism, derivation)-systems in Banach algebras.

Keywords

• additive mapping
• (homomorphism, derivation)-system
• fixed point method
• hyers-ulam stability
• system of additive functional equations
• 47b47
• 17b40
• 39b72
• 47h10