Let A ba a Banach algebra and α, β be automorphisms on A. A linear map d on A is called (α, β)−derivation if d(ab) = α(a)d(b) + d(a)β(b), (a, b ∈ A). In this article we extend Posner’s theorem for (α, β)−derivations d1 and d2. We characterize when the product d1d2 is a (α, β)−derivation.
