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).
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