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Mat. Zametki, 2010, Volume 88, Issue 5, Pages 673–682 (Mi mz8909)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Finite-Increment Theorem for Complex Polynomials

V. N. Dubinin

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

Abstract: For an arbitrary polynomial $P$ of degree at most $n$ and any points $z_1$ and $z_2$ on the complex plane, we establish estimates of the form
$$ |P(z_1)-P(z_2)|\ge d_n|P'(z_1)||z_1-\zeta|, $$
where $\zeta$ is one of the roots of the equation $P(z)=P(z_2)$, and $d_n$ is a positive constant depending only on the number $n$.

Keywords: complex polynomial, finite-increment theorem, Chebyshev polynomial, Zhukovskii function, Markov's inequality, conformal mapping, covering theorem, Steiner symmetrization, conformal capacity

DOI: https://doi.org/10.4213/mzm8909

Full text: PDF file (498 kB)
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English version:
Mathematical Notes, 2010, 88:5, 647–654

Bibliographic databases:

UDC: 512.62+517.54
Received: 29.10.2010
Revised: 27.01.2010

Citation: V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Mat. Zametki, 88:5 (2010), 673–682; Math. Notes, 88:5 (2010), 647–654

Citation in format AMSBIB
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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. 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
    2. Protin F., “Ls Condition For Filled Julia Sets in C”, Ann. Mat. Pura Appl., 197:6 (2018), 1845–1854  crossref  mathscinet  isi  scopus
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