A refinement of an inequality of S. Bernstein
type: Item
instance of: scholarly article
title: A refinement of an inequality of S. Bernstein
zbMATH Open document ID: 0691.30007
DOI: 10.1016/0022-247X(89)90370-3
author: A. Aziz
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let p(z) be a polynomial of degree n. Recently, \textit{C. Frappier}, \textit{Q. I. Rahman} and \textit{S. Ruscheweyh} [Trans. Am. Math. Soc. 288, 69-99 (1985; Zbl 0567.30006)] have shown that \[ (*)\quad_{| z| =1}| p'(z)| \leq n_{1\leq k\leq 2n}| p(e^{ik\pi /n})|. \] In the paper under review, the author shows that the bound in (*) can be considerably improved. In addition, the author obtains a sharp lower bound for the maximum of \(| p'(z)|\) on \(| z| =1\).
reviewed by: George Csordas
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 4130716
zbMATH Keywords: Bernstein inequality
MaRDI profile type: Publication
cites work: Inequalities for polynomials with a prescribed zero
cites work: Simple Proof of a Theorem of Erdos and Lax
cites work: New Inequalities for Polynomials
cites work: Inequalities for Polynomials with a Prescribed Zero
cites work: Proof of a conjecture of P. Erdös on the derivative of a polynomial
cites work: Inequalities of A. Markoff and S. Bernstein for polynomials and related functions
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description: scientific article; zbMATH DE number 4130716