V. N. Dubinin, A. V. Olesov, “Application of conformal mappings to the inequalities for polynomials”, Analytical theory of numbers and theory of functions. Part 18, Zap. Nauchn. Sem. POMI, 286, POMI, St. Petersburg, 2002, 85–102; J. Math. Sci. (N. Y.), 122:6 (2004), 3630

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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 286, Pages 85–102 (Mi znsl1569)

This article is cited in 8 scientific papers (total in 8 papers)

Application of conformal mappings to the inequalities for polynomials

V. N. Dubinin^a, A. V. Olesov^b

^a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
^b Maritime State University named after G. I. Nevelskoi

Full-text PDF (227 kB) Citations (8)

Abstract: Applications of the geometric theory of functions to inequalities for algebraic polynomials are considered. The main attention is paid to constructing a univalent conformal mapping for a given polynomial and to applying the Lebedev and Nehari theorems to this mapping. A new sharp inequality of Bernshtein type for polynomials with restrictions on the growth on a segment or on a circle, inequalities with restrictions on the zeros of the polynomial, and other inequalities are obtained. In particular, classical inequalities by Markov, Bernshtein, and Schur are strengthened.

Received: 19.04.2002

English version:
Journal of Mathematical Sciences (New York), 2004, Volume 122, Issue 6, Pages 3630–3640
DOI: https://doi.org/10.1023/B:JOTH.0000035238.79760.70

Bibliographic databases:

UDC: 512.62+517.54

Language: Russian

Citation: V. N. Dubinin, A. V. Olesov, “Application of conformal mappings to the inequalities for polynomials”, Analytical theory of numbers and theory of functions. Part 18, Zap. Nauchn. Sem. POMI, 286, POMI, St. Petersburg, 2002, 85–102; J. Math. Sci. (N. Y.), 122:6 (2004), 3630–3640

Citation in format AMSBIB

\Bibitem{DubOle02}

\by V.~N.~Dubinin, A.~V.~Olesov

\paper Application of conformal mappings to the inequalities for polynomials

\inbook Analytical theory of numbers and theory of functions. Part~18

\serial Zap. Nauchn. Sem. POMI

\yr 2002

\vol 286

\pages 85--102

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl1569}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1937370}

\zmath{https://zbmath.org/?q=an:1074.30003}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2004

\vol 122

\issue 6

\pages 3630--3640

\crossref{https://doi.org/10.1023/B:JOTH.0000035238.79760.70}

Linking options:

https://www.mathnet.ru/eng/znsl1569

https://www.mathnet.ru/eng/znsl/v286/p85

This publication is cited in the following 8 articles:

Yingxin Cheng, Yanlin Li, Pushpinder Badyal, Kuljeet Singh, Sandeep Sharma, “Conformal Interactions of Osculating Curves on Regular Surfaces in Euclidean 3-Space”, Mathematics, 13:5 (2025), 881
S. I. Kalmykov, “About multipoint distortion theorems for rational functions”, Siberian Math. J., 61:1 (2020), 85–94
S. I. Kalmykov, “On some rational functions which are analogues of Chebyshev polynomials”, J. Math. Sci. (N. Y.), 207:6 (2015), 874–884
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
Kalmykov S.I., “On Some Inequalities for Derivatives of Polynomials and Rational Functions”, Journal of Mathematical Inequalities, 5:1 (2011), 61–69
S. I. Kalmykov, “Majoration principles and some inequalities for polynomials and rational functions with prescribed poles”, J. Math. Sci. (N. Y.), 157:4 (2009), 623–631
V. N. Dubinin, S. I. Kalmykov, “Ekstremalnye svoistva polinomov Chebysheva”, Dalnevost. matem. zhurn., 5:2 (2004), 169–177
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834

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

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