Abstract and Applied Analysis
Volume 2009 (2009), Article ID 437931, 8 pages
doi:10.1155/2009/437931
Research Article

Generalized Hyers-Ulam Stability of Generalized (N,K)-Derivations

M. Eshaghi Gordji,1 J. M. Rassias,2 and N. Ghobadipour1

1Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
2Section of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, 4, Agamemnonos St., Aghia Paraskevi, 15342 Athens, Greece

Received 5 February 2009; Revised 7 April 2009; Accepted 12 May 2009

Academic Editor: Bruce Calvert

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 3≤n, and 3≤k≤n be positive integers. Let A be an algebra and let X be an A-bimodule. A ℂ-linear mapping d:A→X is called a generalized (n,k)-derivation if there exists a (k−1)-derivation δ:A→X such that d(a1a2⋯an)=δ(a1)a2⋯an+a1δ(a2)a3⋯an+⋯+a1a2⋯ak−2δ(ak−1)ak⋯an+a1a2⋯ak−1d(ak)ak+1⋯an+a1a2⋯akd(ak+1)ak+2⋯an+a1a2⋯ak+1d(ak+2)ak+3⋯an+⋯+a1⋯an−1d(an) for all a1,a2,…,an∈A. The main purpose of this paper is to prove the generalized Hyers-Ulam stability of the generalized (n,k)-derivations.