On the zeros and critical points of polynomials with nonnegative coefficients: a nonconvex analogue of the Gauss-Lucas theorem
type: Item
instance of: scholarly article
title: On the zeros and critical points of polynomials with nonnegative coefficients: a nonconvex analogue of the Gauss-Lucas theorem
zbMATH Open document ID: 1380.26010
author: Blagovest Sendov
author: Hristo S. Sendov
published in: Constructive Approximation
publication date: 2017-10-26T00:00:00Z
review text: The Gauss-Lucas theorem claims that the convex hull of the roots of a polynomial contains all the roots of its derivative. The paper extends this result for polynomials with real nonnegative coefficients. If \(S(\varphi)\) is the set af all those complex numbers \(z\), for which \(|\arg (z) |\geq \varphi\), it is shown that whenever a polynomial with nonnegative coefficients has all its roots in \(S(\varphi)\), then all the roots of its derivative lie in the same set.
reviewed by: Vladimír Janiš
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 26D07
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 6798752
zbMATH Keywords: Gauss-Lucas theorem
zbMATH Keywords: zeroes of polynomials
zbMATH Keywords: critical points of polynomials
zbMATH Keywords: convex hull of polynomial roots
MaRDI profile type: Publication
full work available at URL: s00365-017-9374-6
OpenAlex ID: W2606418701
cites work: Q4779788
DOI: 10.1007/S00365-017-9374-6
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description: scientific article; zbMATH DE number 6798752