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.