NEW REGION FOR ZEROS OF A POLAR DERIVATIVE OF POLYNOMIAL
By
R. Mohammad¹ , Mridula Purohit1 and Ab Liman²
¹Department of Mathematics, Vivekananda Global University, Jaipur, Rajasthan, India-303012
Email: shafatruqia@gmail.com, mirdula_purohit@vgu.ac.in
²Department of Mathematics, National Institute of Technology Srinagar, J & K,India-190006
Email: abliman@rediffmail.com
(Received: September 01, 2022; In format: August 31, 2023; Finally Revised: May 06, 2024; Accepted: May 22, 2024)
DOR: https://doi.org/10.58250/jnanabha.2024.54106
Abstract
Let P(z) := Pn j=0 aj z j be a polynomial of degree n. Then by Cauchy’s Classical result, all zeros of P(z) lie in |z| ≤ 1 + max 0≤j≤n−1 | aj an | . In this paper, we shall extend such results to polar derivative of an algebraic polynomial.
2020 Mathematical Sciences Classification: 30C10, 30C15.
Keywords and Phrases: Polar derivative, Polynomial, Zero, Holder’s inequality.