Hyperconvexity and nonexpansive multifunctions

Sine, Robert

doi:10.1090/S0002-9947-1989-0954603-6

Hyperconvexity and nonexpansive multifunctions
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Trans. Amer. Math. Soc. 315 (1989), 755-767 Request permission

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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