Bull. Korean Math. Soc. 2013; 50(1): 305-320
Printed January 31, 2013
https://doi.org/10.4134/BKMS.2013.50.1.305
Copyright © The Korean Mathematical Society.
Hoonjoo Kim
Sehan University
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 $\gamma$-quasiconvexity, maximal elements, topological semilattices with path-connected intervals, collectively fixed point
MSC numbers: 47H10, 47H04, 52A07, 54C60, 54H25
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