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

Bashir Ahmad Zargar, Manzoor Hussain Gulzar, Tawheeda Akhter


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.


inequalities, polar derivative, modulus, coefficients

Subject classification

26D10 ,30C15, 41A17


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