Some Results Concerning Growth of Polynomials

被引：5
|
作者：
Ahmad Zireh [1 ]
E.Khojastehnejhad [1 ]
S.R.Musawi [1 ]
机构：
[1] Department of Mathematics, Shahrood University of Technology
来源：
Analysis in Theory and Applications | 2013年 / 29卷 / 01期
关键词：
Polynomial; inequality; maximum modulus; growth of polynomial;
D O I：
暂无
中图分类号：
O174.14 [多项式理论];
学科分类号：
070104 ;
摘要：
Let P(z) be a polynomial of degree n having no zeros in |z|< 1, then for every real or complex number β with |β|≤ 1, and |z|=1, R ≥ 1, it is proved by Dewan et al. [4] that ︱P(Rz)+ β( R+1/2 )n P(z)︱≤ 1 /2 { (︱Rn + β(R+1/2 )n︱+︱1+ β (R + 1 /2 )n︱) max |z|=1 |P(z)︱-(︱Rn + β (R+1/2 )n︱-︱1+ β(R+1/2 )n︱) min|z|=1 |P(z)︱}.In this paper we generalize the above inequality for polynomials having no zeros in |z|<k, k≤1. Our results generalize certain well-known polynomial inequalities.
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页码：37 / 46
页数：10
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