character amenability and character pseudo-amenability of certain banach algebras

In this paper, we study character amenability of semi-group algebras ℓ^1(s) and weighted semi-group algebras ℓ^1(s,ω), for a certain semi-groups such as right(left) zero semigroup, rectangular band semi-group, band semi-group and uniformly locally finite inverse semi-group. in particular, we show that for a right (left) zero semi-group or a rectangular band semi-group, character amenability, amenability, pseudo - amenability of ℓ^1(s, ω), for each weight ω, are equivalent. we also show that for an archimedean semi-group s, character pseudo - amenability, amenability, approximate amenability and pseudo-amenable of ℓ^1(s) are equivalent.