Sufficient conditions for existence and uniqueness of a Chebyshev center of a nonempty bounded set in a geodesic space

E. N. Sosov

Chair of Geometry, Kazan State University, Kazan, Russia

Abstract: We obtain sufficient conditions for existence and uniqueness of a Chebyshev center of a nonempty bounded set in a geodesic space. We also establish conditions under which the Chebyshev center belongs to the closure of the convex shell of the mentioned set.

Keywords: Chebyshev center, geodesic space.

UDC: 515.124

Received: 21.04.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:6, 39–42

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