关于广义导数的零点位置

Q4 Mathematics
I. A. Wani, Mohammad Hedayetullah Mir, I. Nazir
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引用次数: 1

摘要

设$P(z) =displaystyle prod_{v=1}^n (z-z_v),$是阶为$n的一元多项式$,则$G_gamma[P(z)] =displaystyle sum_{k=1}^n gamma_k prod_{{v=1},{v neq k}}^n (z-z_v),$其中$gamma= (gamma_1,gamma_2,dots,gamma_n)$是一个正实数的n元组,$ sum_{k=1}^n gamma_k = n$是它的广义导数。将经典的关于临界点位置的高斯-卢卡斯定理推广到一类广义导数{g}。本文将Specht定理和A.Aziz引用{1}证明的关于临界点位置的结果推广到广义导数的一类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the location of zeros of generalized derivative
Let $P(z) =displaystyle prod_{v=1}^n (z-z_v),$ be a monic polynomial of degree $n$, then, $G_gamma[P(z)] = displaystyle sum_{k=1}^n gamma_k prod_{{v=1},{v neq k}}^n (z-z_v),$ where $gamma= (gamma_1,gamma_2,dots,gamma_n)$ is a n-tuple of positive real numbers with $sum_{k=1}^n gamma_k = n$, be its generalized derivative. The classical Gauss-Lucas Theorem on the location of critical points have been extended to the class of generalized derivativecite{g}. In this paper, we extend the Specht Theorem and the results proved by A.Aziz cite{1} on the location of critical points to the class of generalized derivative .
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