@article{article_433869, title={On various multimap classes in the KKM theory and their applications}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={2}, pages={88–105}, year={2018}, DOI={10.31197/atnaa.433869}, author={Park, Sehei}, 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}, abstract={<div> <span style="font-size: 12.6px;">Fixed point theory of  </span>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 </div> <div> <span style="font-size: 12.6px;">admissible classes KC, KO in the frame of the KKM theory.  </span>Our aim in this review is to collect the basic properties of our </div> <div> <span style="font-size: 12.6px;">multimap classes and some mutual relations among them in general  </span>topological spaces or our abstract convex spaces. We add some new </div> <div> <span style="font-size: 12.6px;">remarks and further comments to improve many of those results, and  </span>introduce some recent applications of our multimap classes.  </div>}, number={2}, publisher={Erdal KARAPINAR}