On the location of zeros of generalized derivative
نویسندگان
1 Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
2 Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
3 Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
doi
10.22075/ijnaa.2021.22496.2382چکیده
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 .
