On various multimap classes in the KKM theory and their applications

Open Access

Original research article

Author(s):

Sehie Park

The National Academy of Sciences, Republic of Korea, Seoul 06579, and Department of Mathematical Sciences, Seoul National University, Seoul 08826, Korea

Advances in the Theory of Nonlinear Analysis and its Applications 2(2), 88-105.

Received: June 1, 2018

Accepted: June 12, 2018

Published: June 14, 2018

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 A κ c , Better admissible class B , KKM admissible classes

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APA Style

Park, S. (2018). On various multimap classes in the KKM theory and their applications. Advances in the Theory of Nonlinear Analysis and its Application, 2(2), 88-105.