Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Minkowski functional
  • infimal convolution
  • quasiball
  • Banach space
  • distance function
  • antidistance function
  • metric projection
  • metric antiprojection
  • summand of a ball
  • generating set

Mathematics Subject Classification

41A50, 41A65, 52A21

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Suggested citation

M. V. Balashov, G. E. Ivanov. “The Farthest and the Nearest Points of Sets.” Journal of Convex Analysis 25 (2018), No. 3, 1019–1031. https://doi.org/10.68381/jca25065

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.