Journal of Convex Analysis 25 (2018), No. 3, 1019--1031
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
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