Pseudo-amenability and pseudo-contractibility of restricted semigroup algebra

In this article the pseudo-amenability and pseudo-contractibility of restricted semigroup algebra lr1(S)$l_r^1(S)$ and semigroup algebra, l¹(Sr) on restricted semigroup, Sr are investigated for different classes of inverse semi-groups such as Brandt semigroup, and Clifford semigroup. We particularly show the equivalence between pseudo-amenability and character amenability of restricted semigroup algebra on a Clifford semigroup and semigroup algebra on a restricted semigroup. Moreover, we show that when S = M⁰(G, I)is a Brandt semigroup, pseudo-amenability of l¹(Sr) is equivalent to its pseudo-contractibility.