On the characterization and Automatic continuity of (σ, τ)-ternary derivations

Abstract

Let A and B be two algebras, and let sigma, tau : A -> B be two linear mappings. A linear mapping d(1) : A -> B is called a (sigma, tau)-ternary derivation if there exist the linear mappings d(2), d(3) : A -> B which satisfy d(1)(ab) = d(2)(a)sigma(b) +tau(a)d(3)(b) for all a, b is an element of A. By a (d(2), sigma, tau, d(3))-derivation, we mean a (sigma, tau)-ternary derivation d1 associated with the mappings d(2) and d(3). The main purpose of this article is to study the characterization and automatic continuity of such derivations on Banach algebras and C-& lowast;-algebras.