On the maximum modulus of a complex polynomial

IF 0.7 Q2 MATHEMATICS

Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics Pub Date : 2022-09-30 DOI:10.31801/cfsuasmas.989344

S. Malik, Ashish Kumar

引用次数: 0

Abstract

In this paper we impose distinct restrictions on the moduli of the zeros of p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate the dependence of ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 on MαMα and Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p(z)p(z). This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p(1−wn)p(1−wn), $0

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关于复多项式的最大模

本文对p(z)=n∑v=0avzvp(z)=∑v=0navzv的零模施加了明显的限制，研究了∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)∥R>σ≥1R>σ≥1对MαMα和Mα+πMα+π的依赖关系，其中Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)|和p(z)p(z)的某些系数。本文包括了几个结果，特别给出了一些经典的多项式不等式作为特例。此外，估计p(1−wn)p(1−wn)的问题， $0

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