Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39320130701\phi-Amenable and \phi-biflat Banach algebras507515426ENZ.GhorbaniDepertment of Mathematics-University of IsfahanM.Lashkarizadeh BamiDepartment of Mathematics, University of IsfahanJournal Article20110418In this paper we study the concept of ph-biatness of<br />a Banach algebra A, where ph is a continuous homomorphism on A.<br />We prove that if ph is a continuous epimorphism on A and A has<br />a bounded approximate identity and A is ph- bi<br />at, then A is ph-amenable. In the case where ph is an isomorphism on A we show<br />that the ph- amenability of A implies its ph-bi<br />atness.http://bims.iranjournals.ir/article_426_7cc478cf8c3e322dd9f487c878ba4cfc.pdf