Generalized additive functional inequalities in Banach algebras

Document Type : Research Paper


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.


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
\|af(x)+bf(y)+cf(z)\|  \le  \|f(\alpha x+ \beta y+\gamma z)\| .
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).


  • Receive Date: 02 January 2010
  • Revise Date: 11 June 2010
  • Accept Date: 20 June 2010