Let A be a Banach algebra and ,  be continuous homomorphisms on A. Suppose that X be a Banach A-bimodule. A linear mapping d : A −! X is a (,  )-derivation if d(ab) = d(a)(b) +  (a)d(b) (a, b 2 A), and is a (,  )-inner derivation if there exists x 2 X such that d(a) = x(a) −  (a)x (a 2 A). The Banach algebra A is called (,  )-amenable if every (,  )-derivation is (,  )-inner. In this paper, we investigate the relation between amenability and (,  )-amenability of Banach algebras and also hereditary properties of (,  )-amenability. We give the notion -virtual diagonal and -approximate diagonal and apply them in study of -amenability.

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