M. Shams Kojanaghi - Department of Mathematics Science and Research Branch, Islamic Azad University, Tehran of Iran.
Kazem Haghnejad Azar - Department of Mathematics, University of Mohaghegh Ardabili, Ardabil of Iran.
Mohamad Reza Mardanbeigi - Department of Mathematics Science and Research Branch, Islamic Azad University, Tehran of Iran.

Let A be a Banach algebra and X a Banach A-bimodule, the derivation D : A → X is semi-inner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semi-amenable if every derivation D : A → X∗ is semi-inner. The dual Banach algebra A is Connes semi-amenable (resp. approximately semi-amenable) if, every D ∈ Z۱w _ (A,X), for each normal, dual Banach A-bimodule X, is semi -inner (resp. approximately semi-inner). We will investigate on some properties of semi-amenability and Connes semiamenability of Banach algebras which former have been studied for amenability case.

Amenability · Semi-amenablity · Connes-amenability · Connes semi-amenability