Geodesic
Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 3-19

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We establish a number of theorems of geometric approximation theory in asymmetrically normed spaces. Sets with continuous selection of the near-best approximation operator are studied and properties of such sets are discussed in terms of $\delta$-solar points and the distance function. A result on the coincidence of the classes of $\delta$- and $\gamma$-suns in asymmetric spaces is given. An asymmetric analogue of the Kolmogorov criterion for an element of best approximation for suns, strict suns, and $\alpha$-suns is put forward.
Keywords: asymmetric space, continuous selection, approximatively compact set, sun, fixed point. 
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     title = {Some {Classical} {Problems} of {Geometric} {Approximation} {Theory} in {Asymmetric} {Spaces}},
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A. R. Alimov; I. G. Tsar'kov. Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a0/