Document Type : Research Paper

Authors

• Irfan Ahmad Wani
• Mohammad Ibrahim Mir
• Ishfaq Nazir

Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India

Abstract

Let $P(z)={\displaystyle \prod _{v=1}^n(z-z_v),}$ be a monic polynomial of degree $n$, then, $G_{\gamma }[P(z)]={\displaystyle \sum _{k=1}^n{\gamma }_k\prod _{v=1,v\ne k}^n(z-z_v),}$ 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 .

Keywords

• polynomial
• zeros
• critical points and generalized derivative