Abstract and Applied Analysis
Volume 2009 (2009), Article ID 437931, 8 pages
doi:10.1155/2009/437931
Generalized Hyers-Ulam Stability of Generalized (N,K)-Derivations
M.Eshaghi Gordji1
, J.M. Rassias2
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
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.