Some notions of (\sigma, \tau)-amenability for unitization of Banach algebras

Let \mathcal A be a Banach algebra and \sigma and \tau be continuous endomorphisms on \mathcal A. In this paper, we investigate (\sigma, \tau)-amenability and(\sigma, \tau)-weak amenability for unitization of Banach algebras, and also the relation between of them.We introduce and study the concepts (\sigma, \tau)-trace extention property, (\sigma, \tau)-I-weak amenability and (\sigma, \tau)-ideal amenability for \mathcal A and its unitization, where I is a closed two-sided ideal in \mathcal A.