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Zap. Nauchn. Sem. POMI, 2012, Volume 404, Pages 83–99 (Mi znsl5261)  

This article is cited in 1 scientific paper (total in 1 paper)

Some inequalities for polynomials and rational functions associated with a lemniscate

V. N. Dubinin

Far Eastern Federal University, Vladivostok, Russia

Abstract: Inequalities for the area of a lemniscate, and inequalities for polynomials in a lemniscate containing no critical points other than zeros are given. Also, multipoint distortion estimates at the boundary of a lemniscate are proved. Some open problems are discussed. One of them associates with the well-known Smale's mean value conjecture.

Key words and phrases: inequalities for polynomials, distortion estimates, the Smale mean value conjecture.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:1, 45–54

Bibliographic databases:

Document Type: Article
UDC: 512.62+517.54
Received: 05.05.2012

Citation: V. N. Dubinin, “Some inequalities for polynomials and rational functions associated with a lemniscate”, Analytical theory of numbers and theory of functions. Part 27, Zap. Nauchn. Sem. POMI, 404, POMI, St. Petersburg, 2012, 83–99; J. Math. Sci. (N. Y.), 193:1 (2013), 45–54

Citation in format AMSBIB
\Bibitem{Dub12}
\by V.~N.~Dubinin
\paper Some inequalities for polynomials and rational functions associated with a~lemniscate
\inbook Analytical theory of numbers and theory of functions. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 404
\pages 83--99
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5261}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3029594}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 193
\issue 1
\pages 45--54
\crossref{https://doi.org/10.1007/s10958-013-1432-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884984478}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Dubinin, A. S. Afanaseva-Grigoreva, “O lemniskatakh ratsionalnykh funktsii”, Dalnevost. matem. zhurn., 17:2 (2017), 201–209  mathnet  elib
  • Записки научных семинаров ПОМИ
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