Additive s-functional inequality and hom-derivations in Banach algebras

Abstract

In this paper, we introduce and solve the following additive s- functional inequality:

f ( x + y) - f( x) - f( y) = s( f( x - y) - f( x) - f(- y))

where s is a fixed nonzero complex number with | s| < 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in complex Banach algebras.