
Journal of Convex Analysis 20 (2013), No. 1, 093106 Copyright Heldermann Verlag 2013 Weak Convexity of the Distance Function Maxim V. Balashov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny  Moscow 141700, Russia balashov73@mail.ru We investigate the sets which have neighborhood where the distance function from a point to the set is weakly convex. It is shown that such sets are proximally smooth. We obtain precise estimates for parameters of weak convexity via the size of the neighborhood and the constant of proximal smoothness of the set in the Hilbert space. Keywords: Distance function, uniform convexity, uniform smoothness, weak convexity, modulus of weak convexity, proximal smoothness, Psupporting condition. MSC: 49J52, 58C20, 52A07; 52A41, 52A05 [ Fulltextpdf (156 KB)] for subscribers only. 