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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 2, Pages 67–80 (Mi izv379)  

This article is cited in 9 scientific papers (total in 9 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

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.

DOI: https://doi.org/10.4213/im379

Full text: PDF file (1031 kB)
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English version:
Izvestiya: Mathematics, 2002, 66:2, 285–297

Bibliographic databases:

UDC: 517.5
MSC: 26D05, 41A17
Received: 09.01.2001

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
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\crossref{https://doi.org/10.4213/im379}
\mathscinet{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746549436}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Lukashov, “Inequalities for derivatives of rational functions on several intervals”, Izv. Math., 68:3 (2004), 543–565  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. V. Olesov, “Inequalities for majorizing analytical functions”, J. Math. Sci. (N. Y.), 133:6 (2006), 1693–1703  mathnet  crossref  mathscinet  zmath  elib
    3. V. N. Dubinin, “Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition”, Sb. Math., 196:11 (2005), 1605–1625  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95  mathnet  elib
    6. A. M. Meirmanov, “Derivation of equations of seismic and acoustic wave propagation and equations of filtration via homogenization of periodic structures”, Journal of Mathematical Sciences (New York), 2009  crossref  mathscinet  scopus
    7. Qazi M.A. Rahman Q.I., “Some Estimates for the Derivatives of Rational Functions”, Comput. Methods Funct. Theory, 10:1 (2010), 61–79  crossref  mathscinet  zmath  isi
    8. V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. S. I. Kalmykov, “On some rational functions which are analogues of Chebyshev polynomials”, J. Math. Sci. (N. Y.), 207:6 (2015), 874–884  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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