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Izvestiya: Mathematics, 2002, Volume 66, Issue 2, Pages 285–297
DOI: https://doi.org/10.1070/IM2002v066n02ABEH000379 (Mi im379) 		 
This article is cited in 15 scientific papers (total in 15 papers)

On an application of conformal maps to inequalities for rational functions

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (180 kB) Citations (15)
References:
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DOI: https://doi.org/10.1070/IM2002v066n02ABEH000379
Abstract: Using classical properties of conformal maps, we get new exact inequalities for rational functions with prescribed poles. In particular, we prove a new Bernstein-type inequality, an inequality for Blaschke products and a theorem that generalizes the Turan inequality for polynomials. The estimates obtained strengthen some familiar inequalities of Videnskii and Rusak. They are also related to recent results of Borwein, Erdelyi, Li, Mohapatra, Rodriguez, Aziz and others.
Received: 09.01.2001
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2002, Volume 66, Issue 2, Pages 67–80
DOI: https://doi.org/10.4213/im379
Bibliographic databases:
UDC: 517.5
MSC: 26D05, 41A17
Language: English
Original paper language: Russian
Citation: V. N. Dubinin, “On an application of conformal maps to inequalities for rational functions”, Izv. RAN. Ser. Mat., 66:2 (2002), 67–80; Izv. Math., 66:2 (2002), 285–297
Citation in format AMSBIB
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\by V.~N.~Dubinin
\paper On an application of conformal maps to inequalities for rational functions
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 2
\pages 67--80
\mathnet{http://mi.mathnet.ru/im379}
\crossref{https://doi.org/10.4213/im379}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1918844}
\zmath{https://zbmath.org/?q=an:1023.30010}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 2
\pages 285--297
\crossref{https://doi.org/10.1070/IM2002v066n02ABEH000379}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746549436}
Linking options:
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  • https://doi.org/10.1070/IM2002v066n02ABEH000379
  • https://www.mathnet.ru/eng/im/v66/i2/p67
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:703
    Russian version PDF:249
    English version PDF:22
    References:89
    First page:3
     
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