This article is cited in 7 scientific papers (total in 7 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).
PDF file (598 kB)
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
Citation in format AMSBIB
\paper Selections of the metric projection operator and strict solarity of sets with continuous metric projection
\jour Mat. Sb.
\jour Sb. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
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
A. R. Alimov, “Continuity of the metric projection and local solar properties of sets”, Set-Valued Var. Anal., 27:1 (2019), 213–222
A. R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), 76, 11 pp.
A. R. Alimov, “Vypuklost i monotonnaya lineinaya svyaznost mnozhestv s nepreryvnoi metricheskoi proektsiei v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 26, no. 2, 2020, 28–46
I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
|Number of views:|