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Vijñāna Parishad of India

Jñānābha‎, Vol. 54 (1) (2024), (49-52)

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. 

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