I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Mat. Zametki, 110:5 (2021), 773–785; Math. Notes, 110:5 (2021), 773

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Matematicheskie Zametki, 2021, Volume 110, Issue 5, Pages 773–785
DOI: https://doi.org/10.4213/mzm13207 (Mi mzm13207)

This article is cited in 23 scientific papers (total in 23 papers)

Uniform Convexity in Nonsymmetric Spaces

I. G. Tsar'kov

Moscow Center for Fundamental and Applied Mathematics

Full-text PDF (452 kB) Citations (23)

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DOI: https://doi.org/10.4213/mzm13207

Abstract: Uniformly convex asymmetric spaces are defined. It is proved that every nonempty closed convex set in a uniformly convex complete asymmetric space is a set of approximative uniqueness (and, in particular, a Chebyshev set).

Keywords: asymmetric spaces, approximative uniqueness, uniform convexity.

Funding agency	Grant number
Russian Foundation for Basic Research	19-01-00332-a
This work was supported by the Russian Foundation for Basic Research under grant 19-01-00332-a.

Received: 03.07.2021

English version:
Mathematical Notes, 2021, Volume 110, Issue 5, Pages 773–783
DOI: https://doi.org/10.1134/S0001434621110146

Bibliographic databases:

Document Type: Article

UDC: 517.982.256

Language: Russian

Citation: I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Mat. Zametki, 110:5 (2021), 773–785; Math. Notes, 110:5 (2021), 773–783

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Linking options:

https://www.mathnet.ru/eng/mzm13207

https://doi.org/10.4213/mzm13207

https://www.mathnet.ru/eng/mzm/v110/i5/p773

This publication is cited in the following 23 articles:

I. G. Tsarkov, “Svoistva diskretnogo ne bolee chem schetnogo ob'edineniya mnozhestv v nesimmetrichnykh prostranstvakh”, Matem. sb., 216:2 (2025), 128–144
G. E. Ivanov, “Ravnomerno vypuklye mnozhestva v banakhovykh prostranstvakh”, Matem. zametki, 117:2 (2025), 238–256
Tulsi Dass Narang, Sumit Chandok, Sahil Gupta, “On Various Types of Uniform Rotundities”, Annales Mathematicae Silesianae, 2025
I.G. Tsar'kov, “Convexity of $\delta$-Suns and $\gamma$-Suns in Asymmetric Spaces”, Russ. J. Math. Phys., 31:2 (2024), 325
I. G. Tsar'kov, “Uniformly convex cone spaces and properties of convex sets in them”, Math. Notes, 116:4 (2024), 831–840
I.G. Tsarkov, “Relations Between Various Types of Suns in Asymmetric Spaces”, Russ. J. Math. Phys., 31:3 (2024), 562
A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of subspaces in asymmetric normed spaces”, Izv. Math., 88:6 (2024), 1032–1049
Shelly Garg, Harpreet K. Grover, T. D. Narang, “Rotundity of Quotient Spaces in Metric Linear Spaces”, IJMSI, 19:2 (2024), 119
I.G. Tsar'kov, “Local and Global Suns”, Russ. J. Math. Phys., 31:4 (2024), 765
A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
G. A. Akishev, “Neravenstvo raznykh metrik Nikolskogo dlya trigonometricheskikh polinomov v prostranstve so smeshannoi nesimmetrichnoi normoi”, Tr. IMM UrO RAN, 29, no. 4, 2023, 11–26
A. R. Alimov, “Strict protosuns in asymmetric spaces of continuous functions”, Results Math., 78:3 (2023)
I. G. Tsar'kov, “Connectedness in asymmetric spaces”, Journal of Mathematical Analysis and Applications, 527:1 (2023), 127381
I. G. Tsar'kov, “Reflexivity for spaces with extended norm”, Russ. J. Math. Phys., 30:3 (2023), 399
I. G. Tsar'kov, “Continuity of a Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 111:4 (2022), 616–623
A. R. Alimov, I. G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Results Math., 77:2 (2022), 86
A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63:3 (2022), 412–420
I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469

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

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