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 Cipria in Polvere J-weak amenability and ideal amenability, where J is a closed two-sided ideal in A.We also study the hereditary properties of quotient ideal amenability for Banach Water Bottle 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.