This article is cited in 2 papers

The relative Chebyshev center of a finite set in a geodesic space

E. N. Sosov

Kazan State University

Abstract: In the present paper we estimate variation in the relative Chebyshev radius $R_W(M)$, where $M$ and $W$are nonempty bounded sets of a metric space, as the sets $M$ and $W$ change. We find the closure and the interior of the set of all $N$-nets each of which contains its unique relative Chebyshev center, in the set of all $N$-nets of a special geodesic space endowed by the Hausdorff metric. We consider various properties of relative Chebyshev centers of a finite set which lie in this set.

Keywords: relative Chebyshev center, Hausdorff metric, geodesic space.

UDC: 515.124

Received: 17.05.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:4, 59–64

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