
Journal of Convex Analysis 23 (2016), No. 1, 227236 Copyright Heldermann Verlag 2016 Intersection of a Set with a Hyperplane Maxim V. Balashov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny  Moscow region, Russia 141700 balashov73@mail.ru We consider the setvalued mapping whose images are intersections of a fixed closed convex bounded set with nonempty interior from a real Hilbert space with shifts of a closed linear subspace. We characterize such strictly convex sets in the Hilbert space, that the considered setvalued mapping is Hölder continuous with the power 1/2 in the Hausdorff metric. We also consider the question about intersections of a fixed uniformly convex set with shifts of a closed linear subspace. We prove that the modulus of continuity of the setvalued mapping in this case is the inverse function to the modulus of uniform convexity and vice versa: the modulus of uniform convexity of the set is the inverse function to the modulus of continuity of the setvalues mapping. Keywords: Hilbert space, strongly convex set of radius R, Hausdorff metric, Lipschitz continuous setvalued mapping, Hoelder continuous setvalued mapping, modulus of uniform convexity, modulus of continuity. MSC: 49J52, 46C05, 26B25; 46B20, 52A07 [ Fulltextpdf (133 KB)] for subscribers only. 