ADDITIVE s-FUNCTIONAL INEQUALITIES AND PARTIAL MULTIPLIERS IN BANACH ALGEBRAS

Abstract

In this paper, we solve the additive s-functional inequalities

parallel to f(x+y-z) - f(x) - f(y) + f (z) parallel to ˂= parallel to s(f(x-y) + f(y-z) - (x-z))parallel to, (0.1)

where s is a fixed nonzero complex number with vertical bar s vertical bar ˂ 1, and

parallel to(f(x-y) + f(y-z) - f(x-z) parallel to ˂= parallel to s(f(x+y-z) - f(x) - f(y) + f(z))parallel to, (0.2)

where s is a fixed nonzero complex number with vertical bar s vertical bar ˂ 1.

Furthermore, we prove the Hyers-lilam stability of the additive s-functional inequalities (0.1) and (0.2) in complex Banach spaces. This is applied to investigate partial multipliers in Banach (*)-algebras and unital C*-algebras, associated with the additive s -functional inequalities (0.1) and (0.2).