On the Erdös–Lax-Type Inequalities for Polynomials

Pub Date : 2024-08-09 DOI:10.3103/s1068362324700195

I. Nazir, I. A. Wani

引用次数: 0

Abstract

Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject.

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论多项式的厄尔多斯-拉克斯型不等式

摘要 Erdös-Lax 不等式将多项式沿单位圆导数的超规范与多项式本身（在单位圆上）的超规范联系起来。本文旨在利用给定多项式的极值系数，将经典的厄多斯-拉克斯不等式扩展到多项式的极值导数。所获得的结果不仅丰富了 Erdös-Lax 型不等式的领域，而且为这些不等式在各种应用中发挥关键作用提供了一条大有可为的途径。为了说明我们的结果的实际意义，我们举了一个数值例子。它生动地表明，我们的边界比关于这一引人入胜的课题的大量文献中的现有边界要清晰得多。

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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