Bihom derivations in Banach algebras

Abstract

In this paper, we introduce bihom derivations in complex Banach algebras. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of bihom derivations in complex Banach algebras, associated with the bi-additive s-functional inequality f(x+y,z-w)+f(x-y,z+w)-2f(x,z)+2f(y,w)˂= s˂2fx+y2,z-w+2fx-y2,z+w-2f(x,z)+2f(y,w), where s is a fixed nonzero complex number with |s|˂1.