A Fixed Point Theorem for Left Amenable Semi-Topological Semi Groups

Abstract

In this note, we extend and improve the corresponding result of Takahashi. Explanation of DeMarr’s theorem is further generalized for some semi groups of non-expansive self-maps on K by the following considerations which are explained in the paper. The application of Zorn’s lemma and its application are explained. An application of Zorn’s lemma shows that there exists a minimal non-empty compact convex and S-invariant subset.