Additive s-Functional Inequalities

Abstract

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

parallel to f ((k + 1 )x - y) - f (kx - y) - f (x)parallel to <= parallel to s(f (x + y) - f (x) - f (Y))parallel to (0.1)

and

parallel to f (x + y) - f(x) - f(y) parallel to <= parallel to s(f ((k + 1)x - y) - f (kx - y) - f(x))parallel to (0.2)

where k is an integer greater than 1 and s is acomplex number with vertical bar s vertical bar < 1. Furthermore, we prove the Hyers-Ulam stability of the additive s-functional inequalities (0.1) and (0.2) in complex Banach spaces.