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

الملخص EN

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.