Geodesic
The Farthest and the Nearest Points of Sets
Journal of convex analysis, Tome 25 (2018) no. 3, pp. 1019-1031
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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.
Classification : 41A50, 41A65, 52A21
Mots-clés : Minkowski functional, infimal convolution, quasiball, Banach space, distance function, antidistance function, metric projection, metric antiprojection, summand of a ball, generating set 
@article{JCA_2018_25_3_JCA_2018_25_3_a15,
     author = {M. V. Balashov and G. E. Ivanov},
     title = {The {Farthest} and the {Nearest} {Points} of {Sets}},
     journal = {Journal of convex analysis},
     pages = {1019--1031},
     year = {2018},
     volume = {25},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a15/}
}
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M. V. Balashov; G. E. Ivanov. The Farthest and the Nearest Points of Sets. Journal of convex analysis, Tome 25 (2018) no. 3, pp. 1019-1031. http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a15/