I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326

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Sbornik: Mathematics, 2019, Volume 210, Issue 9, Pages 1326–1347
DOI: https://doi.org/10.1070/SM9107 (Mi sm9107)

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

Weakly monotone sets and continuous selection in asymmetric spaces

I. G. Tsar'kov

Lomonosov Moscow State University, Moscow, Russia

English version PDF (560 kB) Citations (23) Russian version article

References:

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DOI: https://doi.org/10.1070/SM9107

Abstract: Sets admitting a continuous selection from the set of near best approximations are studied. Applications of the geometric theory of approximation to the existence of continuous selections for the sets of

$n$ -link piecewise linear functions,

$n$ -link piecewise polynomial functions and generalizations thereof are also discussed.
Bibliography: 23 titles.

Keywords: continuous selection, sun, fixed point.

Funding agency	Grant number
Russian Foundation for Basic Research	19-01-00332-a
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 19-01-00332-a).

Received: 29.03.2018 and 23.10.2018

Bibliographic databases:

Document Type: Article

UDC: 517.982.256

MSC: Primary 41A65; Secondary 47H10

Language: English

Original paper language: Russian

Citation: I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm9107

https://doi.org/10.1070/SM9107

https://www.mathnet.ru/eng/sm/v210/i9/p129

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
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, “Connectedness in asymmetric spaces”, Journal of Mathematical Analysis and Applications, 527:1 (2023), 127381
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
I. G. Tsar'kov, “Reflexivity for spaces with extended norm”, Russ. J. Math. Phys., 30:3 (2023), 399
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
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, “Tomograficheskie kharakterizatsionnye teoremy dlya solnts v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 28, no. 2, 2022, 45–55
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
I. G. Tsarkov, “Uniformly and locally convex asymmetric spaces”, Russ. J. Math. Phys., 29:1 (2022), 141–148
I. G. Tsar'kov, “Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 112:6 (2022), 1017–1024
A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces $C(q)$ and $L^p$ ”, Russ. J. Math. Phys., 29:3 (2022), 291–305
A. R. Alimov, I. G. Tsar’kov, “Suns, moons, and $\mathring{B}$ -complete sets in asymmetric spaces”, Set-Valued Var. Anal., 30:3 (2022), 1233–1245
A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654
I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
A. R. Alimov, I. G. Tsar'kov, “Approximatively Compact Sets in Asymmetric Efimov–Stechkin Spaces and Convexity of Almost Suns”, Math. Notes, 110:6 (2021), 947–951
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

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

Statistics & downloads:
Abstract page:	462
Russian version PDF:	40
English version PDF:	17
References:	45
First page:	6

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