%0 Journal Article
%T On the location of zeros of generalized derivative
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Wani, Irfan Ahmad
%A Mir, Mohammad Ibrahim
%A Nazir, Ishfaq
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 179-184
%! On the location of zeros of generalized derivative
%K Polynomial
%K Zeros
%K critical points and generalized derivative
%R 10.22075/ijnaa.2021.22496.2382
%X 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 .
%U https://ijnaa.semnan.ac.ir/article_5469_c0d5c598e88d64fc2d4a7ca2b1ac5a5c.pdf