Growth of a polynomial with restricted zeros

被引：0
作者：
Abdullah Mir
Abrar Ahmad
Adil Hussain Malik
机构：
[1] University of Kashmir,Department of Mathematics
来源：
The Journal of Analysis | 2020年 / 28卷
关键词：
Polynomial; Maximum modulus; Zeros; 30A10; 30C10; 30C15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we establish some upper bound estimates for the maximal modulus of a polynomial on a disk |z|=R,R≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z|=R, \,R\ge 1$$\end{document}, when there is a restriction on its zeros. The obtained results generalize as well as sharpen some already known estimates due to Govil, Dalal and Govil, Dewan and Bhat and the classical result of Ankeny and Rivlin.
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页码：827 / 839
页数：12
相关论文
共 20 条
[1]  
Ankeny NC(1955)On a theorem of S. Bernstein Pacific Journal of Mathematics 5 849-862
[2]  
Rivlin TJ(1981)Growth of polynomials whose zeros are within or outside a circle Proceedings of the American Mathematical Society 81 549-553
[3]  
Aziz A(1988)Inequalities for a polynomial and its derivative Journal of Approximation Theory 54 306-313
[4]  
Aziz A(2018)On the maximum modulus of polynomials not vanishing in a circle Analysis in Theory and Applications 2018 52-140
[5]  
Dawood QM(1998)On the maximum modulus of polynomials not vanishing inside the unit circle Journal of Interdisciplinary Mathematics 1 129-259
[6]  
Dalal A(1998)On the theorem of Ankeny and Rivlin concerning maximum modulus of polynomials Complex Variables 40 249-631
[7]  
Govil NK(2002)On growth of polynomials Journal of Inequalities and Applications 7 623-82
[8]  
Dewan KK(1989)On the maximum modulus of polynomials not vanishing inside the unit circle Approximation Theory and Its Applications 5 79-500
[9]  
Bhat AA(1987)On Bernstein’s inequality Journal of Mathematical Analysis and Applications 126 494-498
[10]  
Govil NK(2003)Inequalities describing the growth of polynomials not vanishing in a disk of prescribed radius Mathematical Inequalities and Applications 6 491-100
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