This article is cited in 4 scientific papers (total in 4 papers)
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
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.
sun, strict sun, monotone path-connected set, radial continuity of the metric projection.
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Siberian Mathematical Journal, 2017, 58:1, 11–15
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
\paper A monotone path-connected set with outer radially lower continuous metric projection is a~strict sun
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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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
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: continuity of the metric projection and solar properties”, Set-Valued Var. Anal., 27:1 (2019), 213–222
A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
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