On δ-weak φ-amenability of banach algebras

Let A be a Banach algebra and ρ ϵ δ(A) [ f0g. We introduce and study the notion of δ-weak ρ-amenability of Banach algebra A. It is shown that A is δ-weak ρ-amenable if and only if ker(δ) has a bounded δ-weak approximate identity. We prove that every δ-weak ρ-amenable Banach algebra has a bounded δ-weak approximate identity. Finally, we examine this notion for some algebras over locally compact groups and give a characterization of δ-weak ρ-amenability of the Figa-Talamanca-Herz algebras.