Polyhedral approximations of strictly convex compacta

Abstract

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls.

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• Uniform convexity and the splitting problem for selections
• On the splitting problem for selections
• Weakly convex sets and modulus of nonconvexity