This article is cited in 4 scientific papers (total in 4 papers)
Selections of the metric projection operator and strict solarity of sets with continuous metric projection
A. R. Alimov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained.
Bibliography 25 titles.
sun, strict sun, monotone path-connected set, lower semicontinuous metric projection, selection of the metric projection.
|Russian Foundation for Basic Research
|This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00295-a).
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Sbornik: Mathematics, 2017, 208:7, 915–928
MSC: Primary 41A65; Secondary 54C65
Received: 23.06.2016 and 06.02.2017
A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Mat. Sb., 208:7 (2017), 3–18; Sb. Math., 208:7 (2017), 915–928
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\paper Selections of the metric projection operator and strict solarity of sets with continuous metric projection
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:1 (2018), 36–42
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
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
Alimov A.R., “Solarity of Sets in Max-Approximation Problems”, J. Fixed Point Theory Appl., 21:3 (2019), UNSP 76
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