Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 864340, 8 pages
http://dx.doi.org/10.1155/2012/864340
Research Article

Nearly Derivations on Banach Algebras

M. Eshaghi Gordji,1 H. Khodaei,1 and G. H. Kim2

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 11 December 2011; Accepted 23 January 2012

Academic Editor: John Rassias

Copyright © 2012 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 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆 ≠ ( 𝑛 2 − 𝑛 + 4 ) / 2 . We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖ ∑ 1 ≤ 𝑖 < 𝑗 ≤ 𝑛 1 ≤ 𝑘 𝑙 ≠ 𝑖 , 𝑗 ≤ 𝑛 𝑓 ( ( 𝑥 𝑖 + 𝑥 𝑗 ∑ ) / 2 + 𝑛 − 2 𝑙 = 1 𝑥 𝑘 𝑙 ∑ ) + 𝑓 ( 𝑛 𝑖 = 2 𝑥 𝑖 ) + 𝑓 ( 𝑥 1 ∑ ) ‖ ≤ ‖ 𝜆 𝑓 ( 𝑛 𝑖 = 1 𝑥 𝑖 ) ‖ .