Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 870843, 8 pages
doi:10.1155/2009/870843
Research Article

Approximately n-Jordan Homomorphisms on Banach Algebras

M. Eshaghi Gordji,1 T. Karimi,2 and S. Kaboli Gharetapeh3

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Payame Noor University of Fariman Branch, Fariman, Iran
3Department of Mathematics, Payame Noor University of Mashhad Branch, Mashhad, Iran

Received 29 November 2008; Accepted 14 January 2009

Academic Editor: Jong Kim

Copyright © 2009 M. Eshaghi Gordji et al. 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

Let n∈ℕ, and let A, B be two rings. An additive map h:A→B is called n-Jordan homomorphism if h(an)=(h(a))n for all a∈A. In this paper, we establish the Hyers-Ulam-Rassias stability of n-Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism h from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to f, (b) to each approximate n-Jordan homomorphism h between two commutative Banach algebras there corresponds a unique n-ring homomorphism near to f for all n∈{3,4,5}.