A system of biadditive functional equations in Banach algebras

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

Automated summary

In this paper, the general solution and the Hyers-Ulam stability of the system of biadditive functional equations in complex Banach spaces are obtained. Furthermore, the Hyers-Ulam stability of f-biderivations in complex Banach algebras is proved.