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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1410–1415
DOI: https://doi.org/10.17377/semi.2018.15.115 (Mi semr1021) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Real, complex and functional analysis

Distortion theorem for complex polynomials

V. N. Dubininab

a Institute for Applied Mathematics, Far-Eastern Branch of the RAS st. Radio, 7, 690041, Vladivostok, Russia
b Far-Eastern Federal University, st. Sukhanov, 8, 690950, Vladivostok, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.115
Abstract: For any complex polynomial $P$ of degree $n\ge 2$ and any complex number $z$, we consider a sharp inequality involving of the absolute values of $P(z),\; P'(z)$, leading coefficient of $P$ and an upper bound of the moduli of the critical values of $P$. All cases of an equality in this inequality are established.
Keywords: distortion theorems, complex polynomials, inequalities, critical values.
Funding agency Grant number
Russian Science Foundation 14-11-00022
The work is supported by Russian Science Foundation (grant 14-11-00022).
Received November 2, 2018, published November 9, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30C10, 30C85
Language: English
Citation: V. N. Dubinin, “Distortion theorem for complex polynomials”, Sib. Èlektron. Mat. Izv., 15 (2018), 1410–1415
Citation in format AMSBIB
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\by V.~N.~Dubinin
\paper Distortion theorem for complex polynomials
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1410--1415
\mathnet{http://mi.mathnet.ru/semr1021}
\crossref{https://doi.org/10.17377/semi.2018.15.115}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454860200057}
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    • This publication is cited in the following 1 articles:
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