On Sharpening of a Theorem of Ankeny and Rivlin  

作　　者：Aseem Dalal N.K.Govil 

机构地区：[1]Assistant Commissioner of Income Tax,Ministry of Finance,Government of India [2]Department of Mathematics&Statistics,Auburn University,Auburn,AL 36849-5108,USA

出　　处：《Analysis in Theory and Applications》2020年第2期225-234,共10页分析理论与应用（英文刊）

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].

关 键 词：INEQUALITIES POLYNOMIALS ZEROS 

分 类 号：O174.14[理学—数学]