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

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Matematicheskie Zametki, 2002, Volume 71, Issue 2, Pages 261–270
DOI: https://doi.org/10.4213/mzm345 (Mi mzm345)

This article is cited in 17 scientific papers (total in 17 papers)

Uniform Continuity of Generalized Rational Approximations

C. S. Rjutin

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

Full-text PDF (197 kB) Citations (17)

References:

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

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

$\varepsilon$ .

Received: 10.04.2000
Revised: 04.12.2000

English version:
Mathematical Notes, 2002, Volume 71, Issue 2, Pages 236–244
DOI: https://doi.org/10.1023/A:1013915432464

Bibliographic databases:

UDC: 517.51

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm345

https://doi.org/10.4213/mzm345

https://www.mathnet.ru/eng/mzm/v71/i2/p261

This publication is cited in the following 17 articles:

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, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211
I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669
I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
Tsar'kov I.G., “Continuous Selection From the Sets of Best and Near-Best Approximation”, Dokl. Math., 96:1 (2017), 362–364
I. G. Tsarkov, “NEPRERYVNYE VYBORKI IZ MNOZhESTVA BLIZhAIShIKh I POChTI BLIZhAIShIKh TOChEK, “Doklady Akademii nauk””, Doklady Akademii Nauk, 2017, no. 4, 373
I. G. Tsar'kov, “Some applications of geometric theory of approximations”, J. Math. Sci. (N. Y.), 245:1 (2020), 64–82
I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
C. S. Rjutin, “On Uniformly Continuous Almost Best Generalized Rational Approximation Operators”, Math. Notes, 87:1 (2010), 141–145
E. D. Livshits, “On Almost-Best Approximation by Piecewise Polynomial Functions in the Space $C[0,1]$”, Math. Notes, 78:4 (2005), 586–591

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

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