Generalized additive functional inequalities in Banach algebras

Abstract

Using the Hyers-Ulam-Rassias stability method, we<br />investigate isomorphisms in Banach algebras and derivations on<br />Banach algebras associated with the following generalized additive<br />functional inequality<br />begin{eqnarray}<br />|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .<br />end{eqnarray}<br />Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphisms<br />in Banach algebras and of derivations on Banach algebras associated<br />with the generalized additive functional inequality (0.1).