University of TabrizComputational Methods for Differential Equations2345-39827Issue 4 (Special Issue)20190801Some notions of $(\sigma, \tau)-$amenability for unitization of Banach algebras5735799206ENEghbalGhaderiDepartment of Mathematics, University of Kurdistan, Pasdaran Str., P. O. Box 416, Sanandaj, IranSaberNaseriDepartment of Mathematics, University of Kurdistan, Pasdaran Str., P. O. Box 416, Sanandaj, IranJournal Article20190626Let $\mathcal A$ be a Banach algebra and $\sigma$ and $\tau$ be continuous endomorphisms on $\mathcal A$. In this paper, we investigate $(\sigma, \tau)-$amenability and<br />$(\sigma, \tau)-$weak amenability for unitization of Banach algebras, and also the relation between of them.<br />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 $\mathcal A$.https://cmde.tabrizu.ac.ir/article_9206_be620afb824433d40b99035ff0d2affb.pdf