Biderivations and Bihomomorphisms in Banach Algebras

Abstract

In this paper, we solve the following bi-additive s-functional inequalities

parallel to f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) + f(x-y, z-w) - 4f(x, z)parallel to

<= parallel to s(2f(x+y, z-w) + 2f(x-y, z+w) - 4f(x, z) + 4f(y, w)parallel to (1)

and

parallel to 2f(x+y, z-w) + 2f(x-y, z+w) - 4f(x, z) + 4f(y, w)parallel to (2)

<=parallel to f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) + f(x-y, z-w) - 4f(x, z)parallel to,

where s is a fixed nonzero complex number with vertical bar s vertical bar < 1.

Moreover, we prove the Hyers-Ulam stability of biderivations and bihomomorphismsions in Banach algebras and unital C*-algebras, associated with the bi-additive s-functional inequalities (1) and (2).