On one extremal problem for complex polynomials with constraints on critical values
type: Item
instance of: scholarly article
title: On one extremal problem for complex polynomials with constraints on critical values
zbMATH Open document ID: 1303.30002
DOI: 10.1134/S003744661401008X
author: V. N. Dubinin
published in: Siberian Mathematical Journal
publication date: 2014-11-04T00:00:00Z
review text: Let \(P_n\) be the set of all complex polynomials \(P\) of degree \(n\geq 2\) satisfying \(|P(z)|\leq 1\) whenever \(P'(z)=0.\) Using a symmetrisation method, the author proves a result which gives an upper bound for the product \(|P'(0)P'(1)|\), \(P\in P_n\), in terms of certain functions of the values \(|P(0)|\) and \(|P(1)|\). As an application of this result, a number of sharp inequalities for polynomials is presented. In particular, a new version of a Markov-type inequality for an arbitrary compact set is established.
reviewed by: Alexander Ulanovskii
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C85
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 6365602
zbMATH Keywords: Chebyshev polynomial
zbMATH Keywords: critical value
zbMATH Keywords: distortion theorem
zbMATH Keywords: Markov-type inequalities
zbMATH Keywords: symmetrization
MaRDI profile type: Publication
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full work available at URL: s003744661401008x
OpenAlex ID: W2044740967
description: scientific article; zbMATH DE number 6365602