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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 z1 and z2 on the complex plane, we establish estimates of the form
|P(z1)−P(z2)|⩾dn|P′(z1)||z1−ζ|,
where ζ is one of the roots of the equation P(z)=P(z2), and dn 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:
    1. Protin F., “Ls Condition For Filled Julia Sets in C”, Ann. Mat. Pura Appl., 197:6 (2018), 1845–1854  crossref  mathscinet  isi  scopus
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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