This article is cited in 15 scientific papers (total in 15 papers)
I. G. Tsar'kov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
The paper is concerned with properties of sets admitting a continuous selection from the set of nearly best approximations. Necessary and sufficient conditions are put forward for the existence of continuous additive and multiplicative $\varepsilon$-selections on closed sets. Sufficient conditions are given for the existence of continuous selections for stable set-valued mappings with not-necessarily-convex values.
Bibliography: 8 titles.
continuous selection, infinitely connected set, set-valued mapping.
|Russian Foundation for Basic Research
|This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 13-01-00022-a).
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Sbornik: Mathematics, 2016, 207:2, 267–285
MSC: Primary 41A65, 54C65; Secondary 28B20, 54C60
Received: 26.01.2015 and 02.06.2015
I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Mat. Sb., 207:2 (2016), 123–142; Sb. Math., 207:2 (2016), 267–285
Citation in format AMSBIB
\paper Continuous $\varepsilon$-selection
\jour Mat. Sb.
\jour Sb. Math.
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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
I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669
I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
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
I. G. Tsar'kov, “Continuous selection from the sets of best and near-best approximation”, Dokl. Math., 96:1 (2017), 362–364
I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
Alimov A.R., “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
I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
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