Inequalities concerning polynomials having zeros in closed interior of a circle
type: Item
instance of: scholarly article
title: Inequalities concerning polynomials having zeros in closed interior of a circle
zbMATH Open document ID: 0982.30004
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2001-10-23T00:00:00Z
review text: The reviewed paper contains one theorem which is a refinement of some earlier result. Theorem. Let \(p(z)\) be a polynomial of degree \(n\), having all its zeros in \(|z|\leq K\), \(K>1\), then for \(K<R<K^2,\) \[ M\left(p,r\right)\geq r^s\left(\frac{r+K}{1+K}\right)M(p,1)+\frac{r^{n-1}}{K^{n-1}}\left\{\frac{r^{n-s}-1}{Kr^{n-s-1}+1}\right\}m \] where \( M(p,r)=\max_{|z|=r}{|p(z)|}\), \( m=\min_{|z|=K}{|p(z)|} \) and \( s \) is the order of a possible zero of \(p(z)\) at \(z=0\).
reviewed by: Jan Szynal
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 1625167
zbMATH Keywords: inequalities for polynomials
MaRDI profile type: Publication
author: K. K. Dewan
author: Harish Singh
author: R. S. Yadav
description: scientific article; zbMATH DE number 1625167