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The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications. (English) Zbl 0962.47022

A hyperconvex version of the dual form of Knaster-Kuratowski-Mazurkiewicz principle is the main result of this paper. Then, as applications:
1. Ky-Fan-type matching theorems
2. Fixed point theorems (Browder-Fan, Fan-Glickberg)
3. Ky-Fan-type best approximation theorem
4. Intersection theorems (Alexandroff-Pasynkoff, Fan, Klee, Lassonde Horvath)
are proved for the case of hyperconvex spaces.

MSC:

47H04 Set-valued operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
49J35 Existence of solutions for minimax problems
47H10 Fixed-point theorems
52A99 General convexity
54C60 Set-valued maps in general topology
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