Generalized additive functional inequalities in Banach algebras

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in Banach algebras and derivations on Banach algebras associated with the following generalized additive functional inequality\begin{eqnarray}\|af(x)+bf(y)+cf(z)\|  \le  \|f(\alpha x+ \beta y+\gamma z)\| .\end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphism in Banach algebras and of derivations on Banach algebras associated with the generalized additive functional inequality (۰.۱).

Keywords:

Hyers-Ulam-Rassias stability , generalized additive functional inequality , algebra homomorphism in Banach algebra , derivation on Banach algebra