Hyers-ulam stability of the additive s-functional inequality and hom-derivations in banach algebras

Abstract

© 2020 by TJM. All rights reserved. In this work, we solve the following additive s-functional inequality: ‖f(x + y) − f(x) − f(y)‖ ≤ ‖s(f(x − y) − f(x) − f(−y))‖, (0.1) where s is a fixed nonzero complex number with |s| < 1. We prove the HyersUlam stability of the additive s-functional inequality (0.1) in complex Banach spaces by using the fixed point method and the direct method. Moreover, we prove the HyersUlam stability of hom-derivations in complex Banach algebras.