On various multimap classes in the KKM theory and their applications

Year 2018, Volume: 2 Issue: 2, 88 - 105, 30.06.2018

Sehei Park

https://doi.org/10.31197/atnaa.433869

Abstract

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_c^\kappa , 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. 

Keywords

Abstract convex space, (Partial) KKM space, Multimap classes, Fixed point, Admissible multimap class $\frak A_c^\kappa$, Better admissible class $\frak B$, KKM admissible classes

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