Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68229120180801Homomorphism Weak amenability of certain Banach algebras235245309910.22075/ijnaa.2018.1201.1276ENHamidSadeghiDepartment of Mathematics, Faculty of Science, University of Isfahan, Isfahan, IranMahmmodLashkarizadehDepartment of Mathematics, Faculty of Science, University of Isfahan, Isfahan, IranJournal Article20160210In this paper we introduce the notion of $\varphi$-commutativity for a Banach algebra $A$, where $\varphi$ is a continuous homomorphism on $A$ and study the concept of $\varphi$-weak amenability for $\varphi$-commutative Banach algebras. We give an example to show that the class of $\varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We characterize $\varphi$-weak amenability of $\varphi$-commutative Banach algebras and prove some hereditary properties. Moreover we verify some of the previous available results about commutative weakly amenable Banach algebras, for $\varphi$-commutative $\varphi$-weakly amenable Banach algebras.https://ijnaa.semnan.ac.ir/article_3099_3c9686cd0612388fda1d7fbfe656ad40.pdf