phi-Amenable and phi-biflat Banach algebras

In this paper we study the concept of ph-biatness of a Banach algebra A, where ph is a continuous homomorphism on A. We prove that if ph is a continuous epimorphism on A and A has a bounded approximate identity and A is ph- bi at, then A is ph-amenable. In the case where ph is an isomorphism on A we show that the ph- amenability of A implies its ph-bi atness.