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Research Article Approximately n-Jordan Homomorphisms on Banach Algebras | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 870843 8 pages doi 2009 870843 Research Article Approximately n-Jordan Homomorphisms on Banach Algebras M. Eshaghi Gordji 1 T. Karimi 2 and S. Kaboli Gharetapeh3 1 Department of Mathematics Semnan University . Box 35195-363 Semnan Iran 2 Department of Mathematics Payame Noor University ofFariman Branch Fariman Iran 3 Department of Mathematics Payame Noor University of Mashhad Branch Mashhad Iran Correspondence should be addressed to M. Eshaghi Gordji Received 29 November 2008 Accepted 14 January 2009 Recommended by Jong Kim Let n e 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 e 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 e 3 4 5 . 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. 1. Introduction and Preliminaries Let A B be two rings algebras . An additive map h A B is called n-Jordan homomorphism n-ring homomorphism if h an h a n for all a e A h nn 1ai nn 1h aj for all a1 a2 . an e A . If h A B is a linear n-ring homomorphism we say that h is n-homomorphism. The concept of n-homomorphisms was studied for complex algebras by Hejazian et al. 1 see also 2 3 . A 2-Jordan homomorphism is a Jordan homomorphism in the usual sense between rings. Every Jordan homomorphism is an n-Jordan .

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