A system of biadditive functional equations in Banach algebras

Abstract

In this paper, we obtain the general solution and the Hyers-Ulam stability of the system of biadditive functional equations $$\begin{align*} \begin{cases} 2f(x+y,z+w)-g(x,z)-g(x,w)=g(y,z)+g(y,w)\\ g(x+y,z+w)-2f(x-y,z-w)=4f(x,w)+4f(y,z) \end{cases} \end{align*} $$ in complex Banach spaces. Furthermore, we prove the Hyers–Ulam stability of f-biderivations in complex Banach algebras.

Keywords

• hyers–ulam stability
• biadditive mapping
• f-biderivation
• fixed point method
• system of biadditive functional equations