On the inequality of I. Schur
type: Item
instance of: scholarly article
title: On the inequality of I. Schur
zbMATH Open document ID: 0889.41009
author: L. Milev
author: G. Nikolov
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-16T00:00:00Z
review text: The authors extend to the \(k\)-th derivative the well-known Schur inequality by proving that for any polynomial \(f\) of degree at most \(n\) such that \(f(-1) = f(1)=0\) and \(|f|: =\sup |f|([-1,1])\leq 1\) one has \(|f^{(k)} |\leq|\overline T_n^{(k)} |\), where \(\overline T_n(x) =T_n(x \cos (\pi/2n))\) is a modified Chebyshev polynomial. Actually they show that the inequality also holds if the assumption that \(|f|\leq 1\) is replaced by a weaker one that \(|f(\cos (j\pi/n)/ \cos (\pi/2n)) |\leq 1\).
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1115578
zbMATH Keywords: Markov inequality
zbMATH Keywords: Schur inequality
reviewed by: Wiesław Pleśniak
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5658
OpenAlex ID: W2063664610
cites work: Duffin and Schaeffer type inequality for ultraspherical polynomials
cites work: On certain extremal problems for polynomials
cites work: On the inequalities of Bernstein-Markoff for an interval
cites work: Q3278439
cites work: Q4845757
cites work: Q4240907
cites work: On certain Duffin and Schaeffer type inequalities
cites work: Q4054161
cites work: Q4022921
DOI: 10.1006/JMAA.1997.5658
description: scientific article; zbMATH DE number 1115578