Character amenability and character pseudo-amenability of certain Banach algebras

‎In this paper‎, ‎we study character amenability of semigroup algebras `ell^{۱}(S)` and weighted semigroup algebras ell^{۱} (S,omega)‎, ‎for a certain semigroups such as right(left) zero semigroup‎, ‎rectangular band semigroup‎, ‎band semigroup and uniformly locally finite inverse semigroup‎. ‎In particular‎, ‎we show that for a right (left) zero semigroup or a rectangular band semigroup‎, ‎character amenability‎, ‎amenability‎, ‎pseudo‎ - ‎amenability of ell^{۱} (S,omega)‎, ‎for each weight omega ‎, ‎are equivalent‎. ‎We also show that for an archimedean semigroup S ‎, ‎character pseudo‎ - ‎amenability‎, ‎amenability‎, ‎approximate amenability and pseudo-amenable of ell^{۱}(S) are equivalent‎.