TY - JOUR
ID - 5469
TI - On the location of zeros of generalized derivative
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Wani, Irfan Ahmad
AU - Mir, Mohammad Ibrahim
AU - Nazir, Ishfaq
AD - Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
Y1 - 2022
PY - 2022
VL - 13
IS - 1
SP - 179
EP - 184
KW - Polynomial
KW - Zeros
KW - critical points and generalized derivative
DO - 10.22075/ijnaa.2021.22496.2382
N2 - 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 .
UR - https://ijnaa.semnan.ac.ir/article_5469.html
L1 - https://ijnaa.semnan.ac.ir/article_5469_c0d5c598e88d64fc2d4a7ca2b1ac5a5c.pdf
ER -