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

M. Eshaghi Gordji, J. M. Rassias and N. Ghobadipour

Abstract and Applied Analysis, 2009, vol. 2009, issue 1

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.

Date: 2009
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