Additive s-functional inequalities and derivations on Banach algebras

Abstract

In this paper, we introduce the following new additive s-functional inequalities ||f(x - y) + f(y) + f(-x)II ≤ ||s (f(x + y) - f-x) - f(y)) || (0.1) ||f(x + y) - f-x) - f(y)|| ≤ ||s (f(x - y) + f(y) + f(-x)) ||, (0.2) where s is a fixed complex number with |s| < 1, and prove the Hyers-Ulam stability of linear derivations on Banach algebras associated to the additive s-functional inequalities (0.1) and (0.2).