LIE *−DOUBLE DERIVATIONS ON LIE C*−ALGEBRAS

A unital C* – algebra A, endowed with the Lie product [x, y] = xy− yx on A, is called a Lie C* – algebra. Let A be a Lie C* – algebra and g, h : A ! A be C – linear mappings. A C – linear mapping f : A ! A is called a Lie (g, h) – double derivation if f([a, b]) = [f(a), b]+[a, f(b)]+[g(a), h(b)]+[h(a), g(b)] for all a, b 2 A. In this paper, our main purpose is to prove the generalized Hyers - Ulam - Rassias stability of Lie * - double derivations on Lie C* - algebras associated with the following additive mapping: