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 Mat. Sb., 2017, Volume 208, Number 7, Pages 3–18 (Mi msb8765)

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

Abstract: 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.

Keywords: sun, strict sun, monotone path-connected set, lower semicontinuous metric projection, selection of the metric projection.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00295-à This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00295-a).

DOI: https://doi.org/10.4213/sm8765

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English version:
Sbornik: Mathematics, 2017, 208:7, 915–928

Bibliographic databases:

UDC: 517.982.256+517.982.252
MSC: Primary 41A65; Secondary 54C65

Citation: 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

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8765
• https://doi.org/10.4213/sm8765
• http://mi.mathnet.ru/eng/msb/v208/i7/p3

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:1 (2018), 36–42
2. A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
3. 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
4. Alimov A.R., “Solarity of Sets in Max-Approximation Problems”, J. Fixed Point Theory Appl., 21:3 (2019), UNSP 76
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