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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 :AX such that D 1 (ab)=D 2 (a)b+aD 3 (b) for all a,bA. Our aim is to establish the stability of ternary derivation associated with the extended Jensen functional equation

qf k=1 q x k q= k=1 q f(x k )

for all x 1 ,,x q A, where q>1 is a fixed positive integer.

39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
47B47Commutators, derivations, elementary operators, etc.
46H25Normed modules and Banach modules, topological modules