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This article is cited in 21 scientific papers (total in 21 papers)
Connectedness and other geometric properties of suns and Chebyshev sets
A. R. Alimov, I. G. Tsar'kov
Lomonosov Moscow State University
Abstract:
This survey is concerned with structural characteristics of “suns” in normed linear spaces. Special attention is paid to connectedness and monotone path-connectedness of suns. We address both direct theorems of the geometric approximation theory, in which approximative properties of sets are derived from their structural characteristics, and inverse theorems, in which from approximative characteristics of sets one derives their structural properties.
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Journal of Mathematical Sciences (New York), 2016, 217:6, 683–730
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517.982.256
Citation:
A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, Fundam. Prikl. Mat., 19:4 (2014), 21–91; J. Math. Sci., 217:6 (2016), 683–730
Citation in format AMSBIB
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\by A.~R.~Alimov, I.~G.~Tsar'kov
\paper Connectedness and other geometric properties of suns and Chebyshev sets
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 4
\pages 21--91
\mathnet{http://mi.mathnet.ru/fpm1597}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431884}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 217
\issue 6
\pages 683--730
\crossref{https://doi.org/10.1007/s10958-016-3000-1}
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Russian articles,
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This publication is cited in the following articles:
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A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
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I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
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A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
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I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
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A. R. Alimov, “Prostranstva Mazura i 4.3-svoistvo peresecheniya $(BM)$-prostranstv”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:2 (2016), 133–137
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I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669
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I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
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A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928
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A. R. Alimov, “A monotone path-connected set with outer radially lower continuous metric projection is a strict sun”, Siberian Math. J., 58:1 (2017), 11–15
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I. G. Tsar'kov, “Continuous selection from the sets of best and near-best approximation”, Dokl. Math., 96:1 (2017), 362–364
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I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
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I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
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I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
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A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11
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A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
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I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
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I. G. Tsar'kov, “Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function”, Izv. Math., 83:6 (2019), 1234–1258
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I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
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A. R. Alimov, “Continuity of the metric projection and local solar properties of sets: continuity of the metric projection and solar properties”, Set-Valued Var. Anal., 27:1 (2019), 213–222
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I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
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I. G. Tsar'kov, “The Geometry of a Singular Set of Hypersurfaces and the Eikonal Equation”, Math. Notes, 108:3 (2020), 426–433
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