Markov and Bernstein type inequalities for polynomials
type: Item
instance of: scholarly article
title: Markov and Bernstein type inequalities for polynomials
zbMATH Open document ID: 0933.30003
DOI: 10.1155/S1025583499000247
author: N. K. Govil
author: Ram N. Mohapatra
published in: Journal of Inequalities and Applications
publication date: 2000-03-29T00:00:00Z
full work available at URL: https://eudml.org/doc/120160
review text: For a real polynomial \(p(z)= \sum^n_{\nu =0} a_\nu z^\nu\) of degree \(n\) we have the inequality \[ \max_{-1\leq x\leq 1}|p'(x)|\leq n^2\max_{-1\leq x\leq 1}|p(x)| \] which is known as Markov's inequality. For a complex polynomial \(p(z)= \sum^n_{\nu= 0}c_\nu z^\nu\) of degree \(n\) we have \[ \max_{|z|= 1} |p'(z)|\leq n\max_{|z|=1} |p'(z)| \] which is known as Bernstein inequality. Both inequalities are the best possible and are attained for \(T_n(x)= \cos n\cos^{-1}x\) and \(p_n(z)= \lambda z^n\). These two inequalities have been the starting points for many considerations. In this paper, the authors present some of the research centered around these inequalities. The references include more then hundred papers.
reviewed by: Jan Stankiewicz
Mathematics Subject Classification ID: 30A10
Mathematics Subject Classification ID: 26C15
Mathematics Subject Classification ID: 26D05
zbMATH DE Number: 1340269
zbMATH Keywords: Bernstein inequality
MaRDI profile type: Publication
OpenAlex ID: W2086448991
description: scientific article; zbMATH DE number 1340269