Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea.
Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Islamic Republic of Iran.
Using the Hyers-Ulam-Rassias stability method, we
investigate isomorphisms in Banach algebras and derivations on
Banach algebras associated with the following generalized additive
\|af(x)+bf(y)+cf(z)\| \le \|f(\alpha x+ \beta y+\gamma z)\| .
Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphisms
in Banach algebras and of derivations on Banach algebras associated
with the generalized additive functional inequality (0.1).