Geodesic
Max-Solar Properties of Sets in Normed and Asymmetrically Normed Spaces
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 159-174
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The paper is concerned with new concepts of the max-approximation theory related to solar properties of sets: a max-sun, a local max-sun, max-Chebyshev set, and a max-attractor. Some results on max-solarity are established for uniquely remotal sets (such sets are called absolute max-Chebyshev sets). An example of a nonsingleton (nonclosed) uniquely remotal set on an asymmetrically normed plane is constructed, which gives a negative answer in the problem of whether a uniquely remotal set is a singleton (the unique farthest point problem). Results are obtained both in symmetrically and asymmetrically normed spaces.
Classification : 41A65, 52A21, 41A28
Mots-clés : Max-approximation, farthest point, absolutely max-Chebyshev set, uniquely remotal set, max-sun, local max-sun, point of max-luminosity, Chebyshev center 
@article{JCA_2023_30_1_JCA_2023_30_1_a9,
     author = {A. R. Alimov and I. G. Tsar'kov},
     title = {Max-Solar {Properties} of {Sets} in {Normed} and {Asymmetrically} {Normed} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {159--174},
     year = {2023},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a9/}
}
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A. R. Alimov; I. G. Tsar'kov. Max-Solar Properties of Sets in Normed and Asymmetrically Normed Spaces. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 159-174. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a9/