Ulam stability of bihomomorphisms and biderivations in Banach algebras

Abstract

Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of biderivations and bihomomorphisms in Banach algebras and unital C* -algebras, associated with the bi-additive functional inequality:

f(x + y, z + w) + f(x + y, z - w) + f(x - y, z + w) + f(x - y, z - w) - 4f(x, z) = s (2f (x + y, z - w) + 2f (x - y, z + w) - 4f(x, z) + 4f(y, w)), (1) where s is a fixed nonzero complex number with |s| < 1.