Abstract and Applied Analysis
Volume 2010 (2010), Article ID 393247, 12 pages
doi:10.1155/2010/393247
Research Article

Nearly Ring Homomorphisms and Nearly Ring Derivations on Non-Archimedean Banach Algebras

Madjid Eshaghi Gordji1,2,3

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Research Group of Nonlinear Analysis and Applications (RGNAA), Semnan, Iran
3Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran

Received 29 October 2010; Accepted 24 December 2010

Academic Editor: Stephen Clark

Copyright © 2010 Madjid Eshaghi Gordji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the generalized Hyers-Ulam stability of homomorphisms and derivations on non-Archimedean Banach algebras. Moreover, we prove the superstability of homomorphisms on unital non-Archimedean Banach algebras and we investigate the superstability of derivations in non-Archimedean Banach algebras with bounded approximate identity.