Nearly ternary derivations

Abstract

Let A be a normed algebra and X a normed A-birnodule. By a ternary derivation we mean a triple (D(1), D(2), D(3)) of linear mappings D(1), D(2), D(3) A -> X such that D(1) (ab) = D(2)(a)b + aD(3)(b) for all a, b is an element of A. Our aim is to establish the stability of ternary derivations associated with the extended Jensen functional equation qf(Sigma(q)(k=1)xk/q) = Sigma(q)(k=1) f(xk) for all x(1),center dot center dot center dot, x(q) is an element of A, where q > 1 is a fixed positive integer.