Abstract and Applied Analysis
Volume 2012 (2012), Article ID 279632, 11 pages
http://dx.doi.org/10.1155/2012/279632
Research Article

Approximate 𝑛 -Lie Homomorphisms and Jordan 𝑛 -Lie Homomorphisms on 𝑛 -Lie Algebras

M. Eshaghi Gordji1,2 and G. H. Kim1,2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, Republic of Korea

Received 18 October 2011; Accepted 5 January 2012

Academic Editor: Marcia Federson

Copyright © 2012 M. Eshaghi Gordji and G. H. Kim. 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

Using fixed point methods, we establish the stability of 𝑛 -Lie homomorphisms and Jordan 𝑛 -Lie homomorphisms on 𝑛 -Lie algebras associated to the following generalized Jensen functional equation ∑ 𝜇 𝑓 ( 𝑛 𝑖 = 1 𝑥 𝑖 ∑ / 𝑛 ) + 𝜇 𝑛 𝑗 = 2 ∑ 𝑓 ( 𝑛 𝑖 = 1 , 𝑖 ≠ 𝑗 𝑥 𝑖 − ( 𝑛 − 1 ) 𝑥 𝑗 / 𝑛 ) = 𝑓 ( 𝜇 𝑥 1 ) ( 𝑛 ≥ 2 ) .