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 Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 16–21 (Mi smj2835)

A monotone path-connected set with outer radially lower continuous metric projection is a strict sun

A. R. Alimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: A monotone path-connected set is known to be a sun in a finite-dimensional Banach space. We show that a $B$-sun (a set whose intersection with each closed ball is a sun or empty) is a sun. We prove that in this event a $B$-sun with ORL-continuous (outer radially lower continuous) metric projection is a strict sun. This partially converses one well-known result of Brosowski and Deutsch. We also show that a $B$-solar LG-set (a global minimizer) is a $B$-connected strict sun.

Keywords: sun, strict sun, monotone path-connected set, radial continuity of the metric projection.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00295 The author was supported by the Russian Foundation for Basic Research (Grant 16-01-00295).

DOI: https://doi.org/10.17377/smzh.2017.58.102

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English version:
Siberian Mathematical Journal, 2017, 58:1, 11–15

Bibliographic databases:

UDC: 517.982.256+517.982.252
MSC: 35R30

Citation: A. R. Alimov, “A monotone path-connected set with outer radially lower continuous metric projection is a strict sun”, Sibirsk. Mat. Zh., 58:1 (2017), 16–21; Siberian Math. J., 58:1 (2017), 11–15

Citation in format AMSBIB
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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, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928
2. 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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