Inequalities for the polar derivative of a polynomial with restricted zeros

IF 0.5 Q3 MATHEMATICS

Asian-European Journal of Mathematics Pub Date : 2023-06-21 DOI:10.1142/s179355712350167x

W. M. Shah, Raihana Rashid

引用次数: 1

Abstract

Let [Formula: see text] be a polynomial of degree at most [Formula: see text] with real or complex coefficients, then by a prize winning result of Bernstein [Formula: see text] In this paper, we assume that [Formula: see text] has a zero of multiplicity [Formula: see text] at a point inside the unit disc and the remaining zeros outside or inside the disc of radius [Formula: see text] and prove some Bernstein-type inequalities. We also draw the attention of readers to the wrong conclusion of a result due to [Mir and Wani, A note on two recent results about polynomials with restricted zeros, J. Math. Inequalities, 14 (2020) 45–50].

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具有限制零的多项式的极导数的不等式

设[公式:见文]最多是一个具有实数或复系数的次多项式[公式:见文]，那么根据Bernstein[公式:见文]的一个获奖结果，本文假设[公式:见文]在单位圆盘内的某一点上有一个多重性为零[公式:见文]，其余的零点在半径[公式:见文]的圆盘外或圆盘内，并证明了一些Bernstein型不等式。我们还提请读者注意，由于[Mir和Wani，关于两个关于限制零多项式的最近结果的注释，J. Math]而得出的结果的错误结论。贫富差距，14(2020):45-50。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

期刊介绍： Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.