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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 302, Pages 18–37 (Mi znsl915)  
This article is cited in 5 scientific papers (total in 5 papers)

Conformal mappings and inequalities for algebraic polynomials. II

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (244 kB) Citations (5)
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Abstract: This paper supplements the previous paper of the author under the same title. An analog of the Schwarz boundary lemma is proved for non-univalent regular mappings of subsets of the unit disk onto a disk. Based on this result, certain strengthened inequalities of Bernstein type for algebraic polynomials are obtained. The generalized Mendeleev problem is discussed. Two-sided bounds for the module of the derivative of a polynomial with critical points on an interval are established. Bounds for the coefficients of polynomials under certain constraints are provided.
Received: 09.09.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 129, Issue 3, Pages 3823–3834
DOI: https://doi.org/10.1007/s10958-005-0318-5
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, Analytical theory of numbers and theory of functions. Part 19, Zap. Nauchn. Sem. POMI, 302, POMI, St. Petersburg, 2003, 18–37; J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834
Citation in format AMSBIB
\Bibitem{Dub03}
\by V.~N.~Dubinin
\paper Conformal mappings and inequalities for algebraic polynomials.~II
\inbook Analytical theory of numbers and theory of functions. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 302
\pages 18--37
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl915}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2023030}
\zmath{https://zbmath.org/?q=an:1156.30005}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 3
\pages 3823--3834
\crossref{https://doi.org/10.1007/s10958-005-0318-5}
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    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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