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

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 unique Chebyshev center of a nonempty bounded set in a geodesic space belongs to the closure of the convex hull of this set. © 2010 Allerton Press, Inc.