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.

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
$$\begin{array}{r}\Vert af(x)+bf(y)+cf(z)\Vert \le \Vert f(\alpha x+\beta y+\gamma z)\Vert .\end{array}$$
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