On Sharpening of a Theorem of Ankeny and Rivlin

作     者：Aseem Dalal N.K.Govil Aseem Dalal;N.K.Govil

作者机构：Assistant Commissioner of Income TaxMinistry of FinanceGovernment of India Department of Mathematics&StatisticsAuburn UniversityAuburnAL 36849-5108USA 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2020年第36卷第2期

页      面：225-234页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Inequalities polynomials zeros 

摘      要：Let p(z)=∑v^n=0avz^v anzn be a polynomial of degree n,M(p,R)=:max|z|=R≥0|p(z)|and M(p,1)=:||P||.Then according to a well-known result of Ankeny and Rivlin[1],we have for R≥1,M(p,R≤(R^n+1/2)||p||.This inequality has been sharpened by Govil[4],who proved that for R≥1,M(p,R)≤(R^N+1/2)||p||-n/2(||p||^2-4|an|^2/||p||){(R-1)||p||/||p||+2|an|-ln(1+(R-1)||p||/||p||+2|an|)}.In this paper,we sharpen the above inequality of Govil[4],which in turn sharpens the inequality of Ankeny and Rivlin[1].