Derivations into annihilators of the ideals of Banach algebras

In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A.We compare these notions with J-weak amenability and ideal amenability, where J Still Life Art is a closed two-sided ideal Cutlery in A.We also study the hereditary properties of quotient ideal amenability for Banach algebras.Some examples show that the concepts of A/J-weak amenability and of J-weak amenability do not coincide for Banach algebras in general.