Geodesic
Sets with at Most Two-Valued Metric Projection on a~Normed Plane
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 286-301

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We study sets with at most two-valued metric projection in Banach spaces. We show that a two-dimensional Banach space is smooth if and only if every point of the convex hull of an arbitrary closed set with at most two-valued metric projection lies on a segment with endpoints in that set.
Keywords: metric projection, set with at most two-valued metric projection. 
@article{MZM_2017_101_2_a11,
     author = {A. A. Flerov},
     title = {Sets with at {Most} {Two-Valued} {Metric} {Projection} on {a~Normed} {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {286--301},
     publisher = {mathdoc},
     volume = {101},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a11/}
}
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A. A. Flerov. Sets with at Most Two-Valued Metric Projection on a~Normed Plane. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 286-301. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a11/