高斯-卢卡斯定理和多项式的伯恩斯坦型不等式

Pub Date : 2022-12-01 DOI:10.2478/ausm-2022-0013

Liyaqat Ali, N. A. Rather, Suhail Gulzar

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引用次数: 0

摘要

根据高斯-卢卡斯定理，包含多项式的所有零点的凸集也包含多项式的所有临界点。这个结果在多项式解析理论的临界点几何中具有中心重要性。本文得到了高斯-卢卡斯定理的一个推广，并作为应用，建立了bernstein型多项式不等式的一些推广。

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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Gauss Lucas theorem and Bernstein-type inequalities for polynomials

Abstract According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.

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