Academic Editor: Patricia J. Y. Wong
Copyright © 2009 Abbas Najati and Choonkil Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be Banach modules over a -algebra and let be given. We prove the generalized Hyers-Ulam stability of the following functional
equation in Banach modules over a unital -algebra: . We show that if , for some and a mapping satisfies the functional equation mentioned above then the mapping is Cauchy additive. As an application, we investigate homomorphisms in unital -algebras.