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Zbl 1177.39032
Eshaghi Gordji, M.; Rassias, J.M.; Ghobadipour, N.
Generalized Hyers-Ulam stability of generalized $(N,K)$-derivations.
(English)
[J] Abstr. Appl. Anal. 2009, Article ID 437931, 8 p. (2009). ISSN 1085-3375; ISSN 1687-0409/e

Summary: Let $3\le n$, and $3\le k\le n$ be positive integers. Let $A$ be an algebra and let $X$ be an $A$-bimodule. A $\Bbb C$-linear mapping $d:A\to X$ is called a generalized $(n,k)$-derivation if there exists a $(k-1)$-derivation $\delta :A\to X$ such that $d(a_1a_2\dots a_n)=\delta(a_1)a_2\dots a_n+a_1\delta(a_2)a_3\dots a_n+\cdots +a_1a_2\dots a_{k-2}\delta(a_{k-1})a_k\dots a_n+a_1a_2\dots a_{k-1}d(a_k)a_{k+1}\cdots a_n+a_1a_2\dots a_kd(a_{k+1})a_{k+2}\cdots a_n+a_1a_2\cdots a_{k+1}d(a_{k+2})a_{k+3}\cdots a_n+\cdots +a_1\cdots a_{n-1}d(a_n)$ for all $a_1,a_2,\dots,a_n\in A$. The main purpose of this paper is to prove the generalized Hyers-Ulam stability of the generalized $(n,k)$-derivations.
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
47B47 Derivations and linear operators defined by algebraic conditions

Keywords: bimodule; $(n,k)$-derivation; Hyers-Ulam stability

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