- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 2
- On various multimap classes in the KKM theory and their applications
On various multimap classes in the KKM theory and their applications
Authors : Sehei PARK
Pages : 88-105
Doi:10.31197/atnaa.433869
View : 5 | Download : 4
Publication Date : 2018-06-30
Article Type : Other
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