Title of article :
On the location of zeros of generalized derivative
Author/Authors :
Ahmad Wani, Irfan Department of Mathematics - University of Kashmir - South Campus, Anantnag, Jammu and Kashmir, India , Ibrahim Mir, Mohammad Department of Mathematics - University of Kashmir - South Campus, Anantnag, Jammu and Kashmir, India , Nazir, Ishfaq Department of Mathematics - University of Kashmir - South Campus, Anantnag, Jammu and Kashmir, India
Abstract :
Let P(z)=∏ v=1n (z−zv), be a monic polynomial of degree n, then, Gγ [P(z)]=∑k=1nγk ∏ v=1,v≠kn(z−zv), where γ=(γ1,γ2,…,γn) is a n-tuple of positive real numbers with ∑nk=1γk=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
Journal title :
International Journal of Nonlinear Analysis and Applications
