Hyers-Ulam stability; hom-derivation in Banach algebra; additive s-functional inequality; fixed point method; direct method
SPRINGER BASEL AG
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, v. 21, NO 1, UNSP 18
In this paper, we introduce and solve the following additive s- functional inequality:
f ( x + y) - f( x) - f( y) = s( f( x - y) - f( x) - f(- y))
where s is a fixed nonzero complex number with | s| < 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in complex Banach algebras.