Geodesic
Uniformly and locally convex asymmetric spaces
Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1444-1469

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The nonemptyness of the intersections of nested systems of convex bounded closed subsets of uniformly convex asymmetric spaces is studied. The density properties of the points of existence and points of approximative uniqueness are examined for nonempty closed subsets of uniformly convex asymmetric spaces. Problems of the existence and stability of Chebyshev centres are considered; the relationships between $\gamma$-suns, suns and the existence of best approximants are investigated. Sufficient conditions for radial $\delta$-solarity are obtained. Bibliography: 27 titles.
Keywords: asymmetric space, uniformly convex space, Chebyshev centre, approximative uniqueness, convex set, sun. 
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     author = {I. G. Tsar'kov},
     title = {Uniformly and locally convex asymmetric spaces},
     journal = {Sbornik. Mathematics},
     pages = {1444--1469},
     publisher = {mathdoc},
     volume = {213},
     number = {10},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2022_213_10_a5/}
}
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I. G. Tsar'kov. Uniformly and locally convex asymmetric spaces. Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1444-1469. http://geodesic.mathdoc.fr/item/SM_2022_213_10_a5/