
Journal of Convex Analysis 25 (2018), No. 3, 10191031 Copyright Heldermann Verlag 2018 The Farthest and the Nearest Points of Sets Maxim V. Balashov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny  Moscow Region, Russia 141700 balashov73@mail.ru Grigorii E. Ivanov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny  Moscow Region, Russia 141700 g.e.ivanov@mail.ru In a reflexive strictly convex real Banach space we established relationship between the metric projection on some closed convex subset and the metric antiprojection on another ("dual") closed convex subset. Some applications of the result are considered. Keywords: Minkowski functional, infimal convolution, quasiball, Banach space, distance function, antidistance function, metric projection, metric antiprojection, summand of a ball, generating set. MSC: 41A50, 41A65, 52A21 [ Fulltextpdf (117 KB)] for subscribers only. 