%0 Journal Article %T \varphi-amenability of Banach algebras %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Ghaffari, Ali %A Alinejad, Ahmad %D 2012 %\ 09/15/2012 %V 38 %N 3 %P 725-738 %! \varphi-amenability of Banach algebras %K Amenability %K Banach algebras %K $F$-algebra %K $varphi$-amenability %K $varphi$-mean %R %X Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$. %U http://bims.iranjournals.ir/article_237_2d7117eadedb5265aee5e2e415a2034f.pdf