A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366

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Russian Mathematical Surveys, 2018, Volume 73, Issue 2, Pages 366–368
DOI: https://doi.org/10.1070/RM9813 (Mi rm9813)

This article is cited in 9 scientific papers (total in 9 papers)

Brief Communications

Convexity of Chebyshev sets with respect to tangent directions

A. R. Alimov^a, E. V. Shchepin^b

^a Moscow State University
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

English version PDF (353 kB) Citations (9) Russian version article

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DOI: https://doi.org/10.1070/RM9813

Funding agency	Grant number
Russian Foundation for Basic Research	16-01-00295-а
Ministry of Education and Science of the Russian Federation	НШ-6222.2018.1
Russian Science Foundation	14-50-00005
The research of the first author was supported by the Russian Foundation for Basic Research (grant no. 16-01-00295-a) and by the Programme for State Support of Leading Scientific Schools of the President of the Russian Federation (project no. НШ-6222.2018.1). The research of the second author was supported by the Russian Science Foundation under grant no. 14-50-00005 at the Steklov Mathematical Institute of Russian Academy of Sciences. The results in § 1 were obtained by E. V. Shchepin, and the results in § 2, by A. R. Alimov.

Received: 05.12.2017

Bibliographic databases:

Document Type: Article

MSC: 41A65

Language: English

Original paper language: Russian

Citation: A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368

Citation in format AMSBIB

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https://www.mathnet.ru/eng/rm9813

https://doi.org/10.1070/RM9813

https://www.mathnet.ru/eng/rm/v73/i2/p185

This publication is cited in the following 9 articles:

B. B. Bednov, “Finite-Dimensional Spaces where the Class of Chebyshev Sets Coincides with the Class of Closed and Monotone Path-Connected Sets”, Math. Notes, 111:4 (2022), 505–514
A. R. Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii J Math, 43:3 (2022), 519
A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654
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
A. R. Alimov, “Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 209–215
A. R. Alimov, E. V. Shchepin, “Convexity of suns in tangent directions”, Dokl. Math., 99:1 (2019), 14–15
A. R. Alimov, V. E. Shchepin, “Convexity of suns in tangent directions”, J. Convex Anal., 26:4 (2019), 1071–1076
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

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

Statistics & downloads:
Abstract page:	711
Russian version PDF:	86
English version PDF:	26
References:	74
First page:	33

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