Abstract. The main goal of this article is introducing a fairly general framework to treat several types of derivations simultaneously. Let A and B be Banach algebras, and be homomorphisms from A onto B, and X be a Banach B-bimodule. A map D 2 B(A;X) is called an (alpha, beta)-derivation if D(ab) = (a)D(b) + D(a) (b). All homomorphisms, ordinary derivations, skew derivations, and point derivations are certain types of (alpha, beta)-derivations. We de ne (alpha, beta)-analogue of notions of amenability and weak amenability. We show that this notion of amenability behaves very well with constructions such as tensor products and taking second duals.
