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Matematicheskie Zametki, 2021, Volume 110, Issue 1, Pages 29–36
DOI: https://doi.org/10.4213/mzm13181 (Mi mzm13181) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Sharp Inequalities for Rational Functions on a Circle

V. N. Dubininab

a Far Eastern Federal University, Vladivostok
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
Full-text PDF (477 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm13181
Abstract: For rational functions with prescribed poles lying outside the unit circle |z|=1, sharp inequalities are established at points z, |z|=1. In contrast to the known results, the location of the specified poles on either side of the circle |z|=1 is allowed.
Keywords: polynomials, rational functions, Bernstein inequalities, rotation theorems.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00018
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1482-1
The work was carried out with financial support The Russian Foundation for Basic Research (grant no. 20-01-00018) and the Ministry of Education and Science of the Russian Federation (supplementary agreement of 21.04.2020 no. 075-02-2020-1482-1).
Received: 30.12.2020
English version:
Mathematical Notes, 2021, Volume 110, Issue 1, Pages 41–47
DOI: https://doi.org/10.1134/S000143462107004X
Bibliographic databases:
Document Type: Article
UDC: 517.535
Language: Russian
Citation: V. N. Dubinin, “Sharp Inequalities for Rational Functions on a Circle”, Mat. Zametki, 110:1 (2021), 29–36; Math. Notes, 110:1 (2021), 41–47
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm13181
  • https://doi.org/10.4213/mzm13181
  • https://www.mathnet.ru/eng/mzm/v110/i1/p29
    • This publication is cited in the following 4 articles:
    1. Robinson Soraisam, Khangembam Babina Devi, Barchand Chanam, “Some inequalities for rational function with prescribed poles and restricted zeros”, Demonstratio Mathematica, 58:1 (2025)  crossref
    2. A. Mir, T. Fayaz, “Inequalities for a Rational Function with Prescribed Poles”, Sib Math J, 65:4 (2024), 899  crossref
    3. Nisar Ahmad Rather, Mohmmad Shafi Wani, Ishfaq Dar, “Inequalities pertaining to rational functions with prescribed poles”, Ural Math. J., 8:2 (2022), 143–152  mathnet  crossref  mathscinet
    4. A. Mir, S. Hans, “Inequalities concerning rational functions in the complex domain”, Sib. Math. J., 63:5 (2022), 1012  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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