Additive Functional Inequalities in Banach Modules

Abstract

We investigate the following functional inequality parallel to 2f (x) + 2f (y) + 2f (z) - f (x + y) - f (y + z) parallel to <= parallel to f (x + z) parallel to in Banach modules over a C*-algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a C*-algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.