Best approximations of convex compact sets by balls in the Hausdorff metric
An upper bound for the Hausdorff distance between a nonempty bounded set and the set of all closed balls in a strictly convex straight geodesic space \(X\) of nonnegative curvature is obtained. It is also proved that the set \(\chi[M]\) of centers of the closed balls approximating a convex compact set \(M\) is nonempty and contained in \(M\). The authors also study some other properties of \(\chi[M]\). These results extend some results due to \textit{S. I. Dudov} and \textit{I. V. Zlatorunskaya} [Sb. Math. 191, No. 10, 1433--1458 (2000); translation from Mat. Sb. 191, No. 10, 13--38 (2000; Zbl 0981.52005)] to the case of a strictly convex straight geodesic space.
scientific article; zbMATH DE number 2121460