Additive functional equations and partial multipliers in $$C^*$$ C ∗ -algebras

Abstract

In this paper, we solve the additive functional equations and where s is a fixed nonzero complex number. Furthermore, we prove the Hyers–Ulam stability of the additive functional equations (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 equations (1) and (2).