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Mat. Sb., 2019, Volume 210, Number 9, Pages 129–152 (Mi msb9107)  

This article is cited in 3 scientific papers (total in 3 papers)

Weakly monotone sets and continuous selection in asymmetric spaces

I. G. Tsar'kov

Lomonosov Moscow State University, Moscow, Russia

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).


DOI: https://doi.org/10.4213/sm9107

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English version:
Sbornik: Mathematics, 2019, 210:9, 1326–1347

Bibliographic databases:

UDC: 517.982.256
MSC: Primary 41A65; Secondary 47H10
Received: 29.03.2018 and 23.10.2018

Citation: I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Mat. Sb., 210:9 (2019), 129–152; Sb. Math., 210:9 (2019), 1326–1347

Citation in format AMSBIB
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\pages 1326--1347
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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. Alimov A.R., “Solarity of Sets in Max-Approximation Problems”, J. Fixed Point Theory Appl., 21:3 (2019), UNSP 76  crossref  mathscinet  isi
    2. 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  mathnet  crossref  elib
    3. A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317  mathnet  crossref  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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