Abstract
We investigate the following functional inequality in Banach modules over a
-algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a
-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.