
Journal of Convex Analysis 25 (2018), No. 3, [final page numbers not yet available] 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: Weak convexity, Minkowski functional, infimal convolution, quasiball, weak convexity, Minkowski functional, infimal convolution, quasiball, Banach space, distance function, antidistance function, metric projection, metric antiprojection, summand of a ball MSC: 41A50, 41A65, 52A21 [ Fulltextpdf (314 KB)] for subscribers only. 