APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES

Title & Authors
APPLICATIONS OF RESULTS ON ABSTRACT CONVEX SPACES TO TOPOLOGICAL ORDERED SPACES
Kim, Hoonjoo;

Abstract
Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..
Keywords
abstract convex space;KKM map;generalized KKM;generalized;$\small{{\gamma}}$-quasiconvexity;maximal elements;topological semilattices with path-connected intervals;collectively fixed point;
Language
English
Cited by
1.
GENERALIZED KKM-TYPE THEOREMS FOR BEST PROXIMITY POINTS,;

대한수학회보, 2016. vol.53. 5, pp.1363-1371
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