On the location of zeros of generalized derivative

	On the location of zeros of generalized derivative
International Journal of Nonlinear Analysis and Applications
مقاله 14، دوره 13، شماره 1، خرداد 2022، صفحه 179-184 اصل مقاله (319.3 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22496.2382
نویسندگان
Irfan Ahmad Wani^* ؛ Mohammad Ibrahim Mir؛ Ishfaq Nazir
Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
چکیده
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 derivative\cite{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 .
کلیدواژه‌ها
polynomial؛ zeros؛ critical points and generalized derivative
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