Bihomomorphisms and biderivations in Lie Banach algebras

Abstract

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

parallel to f(x -y,y+ z)+ f(y+ z,z - x)+ f(z + x, x - z)-f(x-y,x+y)parallel to (0,1)

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

where s is a fixed nonzero complex number satisfying vertical bar s vertical bar< 1. Furthermore, we prove the Hyers-Ulam stability of bihomomorphisms and biderivations in Lie Banach algebras associated with the bi-additive s-functional inequality (0.1).