University of Tabriz Computational Methods for Differential Equations 2345-3982 7 Issue 4 (Special Issue) 2019 08 01 Some notions of $(\sigma, \tau)-$amenability for unitization of Banach algebras 573 579 9206 EN Eghbal Ghaderi Department of Mathematics, University of Kurdistan, Pasdaran Str., P. O. Box 416, Sanandaj, Iran Saber Naseri Department of Mathematics, University of Kurdistan, Pasdaran Str., P. O. Box 416, Sanandaj, Iran Journal Article 2019 06 26 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<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