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Mat. Zametki, 2002, Volume 71, Issue 2, Pages 261–270 (Mi mz345)  

This article is cited in 13 scientific papers (total in 13 papers)

Uniform Continuity of Generalized Rational Approximations

C. S. Rjutin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, it is shown that there are no uniformly continuous multiplicative $\varepsilon$-selections from $C[0,1]$ on the set of generalized rational fractions of sufficiently general form for small $\varepsilon$.

DOI: https://doi.org/10.4213/mzm345

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English version:
Mathematical Notes, 2002, 71:2, 236–244

Bibliographic databases:

UDC: 517.51
Received: 10.04.2000
Revised: 04.12.2000

Citation: C. S. Rjutin, “Uniform Continuity of Generalized Rational Approximations”, Mat. Zametki, 71:2 (2002), 261–270; Math. Notes, 71:2 (2002), 236–244

Citation in format AMSBIB
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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. E. D. Livshits, “On Almost-Best Approximation by Piecewise Polynomial Functions in the Space $C[0,1]$”, Math. Notes, 78:4 (2005), 586–591  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. C. S. Rjutin, “On Uniformly Continuous Almost Best Generalized Rational Approximation Operators”, Math. Notes, 87:1 (2010), 141–145  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Tsar'kov I.G., “Continuous Selection From the Sets of Best and Near-Best Approximation”, Dokl. Math., 96:1 (2017), 362–364  crossref  mathscinet  zmath  isi  scopus  scopus
    8. I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859  mathnet  crossref  crossref  adsnasa  isi  elib
    9. I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579  mathnet  crossref  crossref  adsnasa  isi  elib
    10. I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734  mathnet  crossref  crossref  isi  elib
    11. I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238  mathnet  crossref  crossref  isi  elib
    12. I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008  mathnet  crossref  crossref  isi
    13. I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347  mathnet  crossref  crossref  adsnasa  isi
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