ADDITIVE s-FUNCTIONAL INEQUALITIES AND PARTIAL MULTIPLIERS IN BANACH ALGEBRAS

Abstract

In this paper, we solve the additive s -functional inequalities ‖ f (x+y-z)- f (x)- f (y)+ f (z)‖ ≤ ‖s( f (x-y)+ f (y-z)- f (x-z))‖, (0.1) where s is a fixed nonzero complex number with |s| < 1, and ‖ f (x-y)+ f (y-z)- f (x-z)‖ ≤ ‖s( f (x+y-z)- f (x)- f (y)+ f (z))‖, (0.2) where s is a fixed nonzero complex number with |s| < 1. Furthermore, we prove the Hyers-Ulam 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).