Fixed points and partial multipliers in Banach algebras

Abstract

In this paper, we solve the additive functional inequalities where s is a fixed nonzero complex number with vertical bar s vertical bar < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive functional inequalities (1) and (2) in complex Banach spaces. This is applied to investigate partial multipliers in Banach*-algebras, unital C*-algebras, Lie C*-algebras, JC*-algebras and C*-ternary algebras, associated with the additive functional inequalities (1) and (2).