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Zbl 1141.39024
Amyari, Maryam; Baak, Choonkil; Moslehian, Mohammad Sal
Nearly ternary derivations. (English)
[J] Taiwanese J. Math. 11, No. 5, 1417-1424 (2007). ISSN 1027-5487

Authors' abstract: Let $A$ be a normed algebra and $X$ a normed $A$-bimodule. By a ternary derivation we mean a triple $ (D_1, D_2, D_3)$ of linear mappings $D_1, D_ 2, D_3 : A \to X$ such that $ D_1 (ab) = D_2 (a) b + a D_3 (b)$ for all $ a,b \in A$. Our aim is to establish the stability of ternary derivation associated with the extended Jensen functional equation $$ qf \left( { \sum_{k=1}^q x_k } \over q \right) = \sum_{k=1}^q f (x_k) $$ for all $x_1,\dots, x_q \in A$, where $ q> 1$ is a fixed positive integer.
[Claudi Alsina (Barcelona)]

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
46H25 Topological modules

Keywords: Hyers-Ulam-Rassias stability; ternary derivations; extendend Jensen equation; normed algebra; normed $A$-bimodule

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