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Matematicheskie Zametki, 2010, Volume 88, Issue 5, Pages 673–682
DOI: https://doi.org/10.4213/mzm8909 (Mi mzm8909) 		 
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
Full-text PDF (498 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8909
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.
Received: 29.10.2010
Revised: 27.01.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 5, Pages 647–654
DOI: https://doi.org/10.1134/S0001434610110040
Bibliographic databases:
Document Type: Article
UDC: 512.62+517.54
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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