Korean J. Math. Vol. 29 No. 3 (2021) pp.631-638
DOI: https://doi.org/10.11568/kjm.2021.29.3.631

Inequalities concerning polynomial and its derivative

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Published: Sep 30, 2021
Keywords:
inequalities, polar derivative, modulus, coefficients
Mathematics Subject Classification:
26D10, 30C15, 41A17

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Bashir Ahmad Zargar
Department of Mathematics, University of Kashmir, Srinagar-190006, India
Manzoor Hussain Gulzar
Department of Mathematics, University of Kashmir, Srinagar-190006, India
Tawheeda Akhter
Department of Mathematics, University of Kashmir, Srinagar-190006, India

Abstract

In this paper, some sharp inequalities for ordinary derivative $P'(z)$ and polar derivative $D_\alpha P(z)=nP(z)+(\alpha-z)P'(z)$ are obtained by including some of the coefficients and modulus of each individual zero of a polynomial $P(z)$ of degree $n$ not vanishing in the region $|z|>k$, $k\geq 1$. Our results also improve the bounds of Tur\'an's and Aziz's inequalities.



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