Abstract
AbstractAgeneralized metric type spaceis a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.
Highlights
The KKM theory, rst called by the author in 1992 [17], is the study on applications of equivalent formulations or generalizations of the KKM theorem due to Knaster, Kuratowski, and Mazurkiewicz in 1929
The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory
: The main purpose of this paper is to study some topological nature of circular metric spaces and deduce some xed point theorems for maps satisfying the KKM property
Summary
The KKM theory, rst called by the author in 1992 [17], is the study on applications of equivalent formulations or generalizations of the KKM theorem due to Knaster, Kuratowski, and Mazurkiewicz in 1929. In the last decade, many authors obtained some KKM theoretic results on hyperconvex metric spaces as well as newly de ned spaces like NR-metric spaces, metric type spaces, cone metric spaces, cone b-metric spaces, tvs-cone metric spaces, circular metric spaces, modular metric spaces, convex metric spaces, etc. These type of spaces may be called generalized metric type spaces as a generic name.
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