Properties of two selections in metric spaces of nonpositive curvature. (English) Zbl 1162.53057
Given a metric space \(H\), let \(B(H)\) denote the class of all non-empty bounded closed subsets of \(H\). In this paper, the results include the following:
Result 1: In any fininite-dimensional strictly convex metric space \(H\), the Chebyshev centre is unique and the radius of the set \(V\) in \(B(H)\) can be determined by a finite number of points from \(V\).
Result 2: Let \(H\) be any strictly convex space of Busemann nonpositive curvature. Then the upper bound for the power of the generalized Hölder map \(\text{cheb}: B(H)\to H\) is \({1\over 2}\).
Result 1: In any fininite-dimensional strictly convex metric space \(H\), the Chebyshev centre is unique and the radius of the set \(V\) in \(B(H)\) can be determined by a finite number of points from \(V\).
Result 2: Let \(H\) be any strictly convex space of Busemann nonpositive curvature. Then the upper bound for the power of the generalized Hölder map \(\text{cheb}: B(H)\to H\) is \({1\over 2}\).
Reviewer: K. Chandrasekhara Rao (Kumbakonam)
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