# zbMATH — the first resource for mathematics

Nearly ternary derivations. (English) Zbl 1141.39024
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.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 47B47 Commutators, derivations, elementary operators, etc. 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Full Text: