Generalized additive functional inequalities in Banach algebras

Park, C.; Najati, A.

doi:10.22075/ijnaa.2010.75

Generalized additive functional inequalities in Banach algebras

Document Type : Research Paper

Authors

C. Park ¹

A. Najati ²

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.

10.22075/ijnaa.2010.75

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

Keywords

Hyers-Ulam-Rassias stability

generalized additive functional inequality

algebra homomorphism in Banach algebra

derivation on Banach algebra