Generalized additive functional inequalities in Banach algebras

Authors

1 Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea.

2 Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Islamic Republic of Iran.

Abstract

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 homomorphisms
in Banach algebras and of derivations on Banach algebras associated
with the generalized additive functional inequality (0.1).

Keywords