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Hyperconvexity and nonexpansive multifunctions

Author: Robert Sine
Journal: Trans. Amer. Math. Soc. 315 (1989), 755-767
MSC: Primary 54C65; Secondary 47H09, 47H10, 54G05
MathSciNet review: 954603
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Abstract: It is shown that a ball intersection valued nonexpansive multifunction on a hyperconvex space admits a nonexpansive point valued selection. This implies fixed point theorems for such multifunctions and to certain point valued nonexpansive maps. The result is used to study best approximation and to show the space of all nonexpansive maps of a bounded hyperconvex space is hyperconvex.

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Keywords: Multifunction, selection, fixed point, retract, best approximation, nonexpansive, hyperconvex
Article copyright: © Copyright 1989 American Mathematical Society

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