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 $$|s|<1$$. 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).