ON VARIOUS MULTIMAP CLASSES IN THE KKM THEORY AND THEIR APPLICATIONS

Fixed point theory of convex-valued multimaps are closely related to the KKM theory from the beginning. In the last twenty-five years, we introduced the acyclic multimap class, the admissible multimap class A^κ_c , the better admissible class B, and the KKM admissible classes KC, KO in the frame of the KKM theory. Our aim in this review is to collect the basic properties of our multimap classes and some mutual relations among them in general topological spaces or our abstract convex spaces. We add some new remarks and further comments to improve many of those results, and introduce some recent applications of our multimap classes.