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Matematicheskie Zametki, 2012, Volume 91, Issue 5, Pages 761–772
DOI: https://doi.org/10.4213/mzm8759 (Mi mzm8759) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Approximation to the Function zα by Rational Fractions in a Domain with Zero External Angle

A. A. Pekarskii

Belarusian State Technological University
Full-text PDF (525 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm8759
Abstract: Rational approximations to the function zα, α∈R∖Z, were studied by Newman, Gonchar, Bulanov, Vyacheslavov, Andersson, Stahl, and others. The present paper deals with the order of best rational approximations to this function in a domain with zero external angle and vertex at the point z=0. In particular, the obtained results show that the conditions imposed on the boundary of the domain in the Jackson-type inequality proved by the author in 2001 for the best rational approximations in Smirnov spaces cannot be weakened significantly.
Keywords: best uniform rational approximation, polynomial approximation, Smirnov space, analytic function, rational function, rectifiable Jordan boundary, Lavrentiev curve.
Received: 08.03.2010
Revised: 18.03.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 5, Pages 714–724
DOI: https://doi.org/10.1134/S0001434612050136
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. A. Pekarskii, “Approximation to the Function zα by Rational Fractions in a Domain with Zero External Angle”, Mat. Zametki, 91:5 (2012), 761–772; Math. Notes, 91:5 (2012), 714–724
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm8759
  • https://www.mathnet.ru/eng/mzm/v91/i5/p761
    • This publication is cited in the following 5 articles:
    1. P. G. Potseiko, Y. A. Rovba, “On Estimates of Uniform Approximations by Rational Fourier–Chebyshev Integral Operators for a Certain Choice of Poles”, Math. Notes, 113:6 (2023), 815–830  mathnet  crossref  crossref  mathscinet
    2. Yipei Zhang, Guixiang Wang, 2021 2nd International Conference on Artificial Intelligence and Information Systems, 2021, 1  crossref
    3. Wang G., Shen Ch., Wang Ya., “Approximation of Fuzzy Numbers By Using Multi-Knots Piecewise Linear Fuzzy Numbers”, J. Intell. Fuzzy Syst., 39:3 (2020), 3597–3615  crossref  isi
    4. Chenjie Shen, Guixiang Wang, Yifeng Xu, Advances in Intelligent Systems and Computing, 1074, Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery, 2020, 686  crossref
    5. G. Wang, J. Li, “Approximations of fuzzy numbers by step type fuzzy numbers”, Fuzzy Sets and Systems, 310 (2017), 47–59  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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