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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 1, Pages 107–119
DOI: https://doi.org/10.33048/smzh.2020.61.107 (Mi smj5967) 		 
This article is cited in 7 scientific papers (total in 7 papers)

About multipoint distortion theorems for rational functions

S. I. Kalmykovab

a School of Mathematical Sciences, Shanghai Jiao Tong University
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
Full-text PDF (421 kB) Citations (7)
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DOI: https://doi.org/10.33048/smzh.2020.61.107
Abstract: We prove some two- and three-point distortion theorems for rational functions that generalize some recent results on Bernstein-type inequalities for polynomials and rational functions. The rational functions under study have either majorants or restrictions on location of their zeros. The proofs are based on the new version of the Schwarz Lemma and univalence condition for regular functions which was suggested by Dubinin.
Keywords: rational functions, Bernstein-type inequalities, multipoint distortion theorems, univalent functions.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00101_мол_а
The author was supported by the Russian Foundation for Basic Research (Grant 18-31-00101 mol-a).
Received: 15.02.2019
Revised: 25.03.2019
Accepted: 15.05.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 1, Pages 85–94
DOI: https://doi.org/10.1134/S0037446620010073
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: S. I. Kalmykov, “About multipoint distortion theorems for rational functions”, Sibirsk. Mat. Zh., 61:1 (2020), 107–119; Siberian Math. J., 61:1 (2020), 85–94
Citation in format AMSBIB
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\by S.~I.~Kalmykov
\paper About multipoint distortion~ theorems for rational functions
\jour Sibirsk. Mat. Zh.
\yr 2020
\vol 61
\issue 1
\pages 107--119
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\crossref{https://doi.org/10.33048/smzh.2020.61.107}
\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 1
\pages 85--94
\crossref{https://doi.org/10.1134/S0037446620010073}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000516567300007}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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    References:43
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