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Zap. Nauchn. Sem. POMI, 2008, Volume 357, Pages 143–157 (Mi znsl2123)  

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

Majoration principles and some inequalities for polynomials and rational functions with prescribed poles

S. I. Kalmykov

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The paper considers the equality cases in the majoration principle for meromorphic functions established earlier by V. N. Dubinin and S. I. Kalmykov [Mat. Sb. 198:12 (2007), 37–46; translated in Sb. Math. 198:11–12 (2007), 1737–1745]. As corollaries of this principle, we obtain new inequalities for the coefficients and derivatives of polynomials satisfying certain conditions on two intervals. Simple proofs of some Lukashov's theorems on the derivatives of rational functions on several intervals [MR 2069196 (2006):26010)] are provided. Bibl. – 13 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 157:4, 623–631

Bibliographic databases:

UDC: 517.54
Received: 07.07.2008

Citation: S. I. Kalmykov, “Majoration principles and some inequalities for polynomials and rational functions with prescribed poles”, Analytical theory of numbers and theory of functions. Part 23, Zap. Nauchn. Sem. POMI, 357, POMI, St. Petersburg, 2008, 143–157; J. Math. Sci. (N. Y.), 157:4 (2009), 623–631

Citation in format AMSBIB
\Bibitem{Kal08}
\by S.~I.~Kalmykov
\paper Majoration principles and some inequalities for polynomials and rational functions with prescribed poles
\inbook Analytical theory of numbers and theory of functions. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 357
\pages 143--157
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2123}
\zmath{https://zbmath.org/?q=an:1182.30041}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 157
\issue 4
\pages 623--631
\crossref{https://doi.org/10.1007/s10958-009-9343-0}


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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. S. I. Kalmykov, “Polynomials with curved majorants on two segments”, Russian Math. (Iz. VUZ), 53:10 (2009), 64–67  mathnet  crossref  mathscinet  zmath  elib
    2. S. I. Kalmykov, “Covering theorems for polynomials with curved majorants on two segments”, J. Math. Sci. (N. Y.), 178:2 (2011), 170–177  mathnet  crossref
    3. V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, J. Math. Sci. (N. Y.), 184:6 (2012), 703–708  mathnet  crossref
    4. 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
    5. S. I. Kalmykov, “On polynomials and rational functions normalized on the circular arcs”, J. Math. Sci. (N. Y.), 200:5 (2014), 577–585  mathnet  crossref
    6. A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Sb. Math., 205:10 (2014), 1413–1441  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. Kalmykov S.I., Nagy B., “Polynomial and Rational Inequalities on Analytic Jordan Arcs and Domains”, J. Math. Anal. Appl., 430:2 (2015), 874–894  crossref  mathscinet  zmath  isi  elib  scopus
    9. Akturk M.A., Lukashov A., “Sharp Markov-type inequalities for rational functions on several intervals”, J. Math. Anal. Appl., 436:2 (2016), 1017–1022  crossref  mathscinet  zmath  isi  elib  scopus
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