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In this writing we investigates module amenability from a different angle.Here the concept of module amenability (more precisely -amenability) is defined for a Banach module E over a Banach algebra A with a given bounded Banach A-module homomorphism :E- A. Also we introduce and study the concepts of approximate -amenability, -contractibility, -phi-amenability and -phi-contractibility, of a Banach A-module E, where phi is a character on A.