# Inequalities for the polar derivative of a polynomial

• M. H. Gulzar
• B. A. Zargar
• Rubia Akhter
Original Research Paper

## Abstract

Let P(z) be a polynomial of degree n having all its zeros in $$|z|\le 1$$, then according to Turan (Compositio Mathematica 7:89–95, 2004)
\begin{aligned} \max \limits _{|Z|=1}|P'(z)|\ge \frac{n}{2}\max \limits _{|Z|=1}|P(z)|. \end{aligned}
In this paper, we shall use polar derivative and establish a generalisation and an extension of this result. Our results also generalize variety of other results.

## Keywords

Polynomial Polar derivative Inequalities

30A10 30C15

## Notes

### Acknowledgements

This work was supported by NBHM, India, under the research project number 02011/36/2017/R&D-II.

### Conflict of interest

The authors declare that they have no conflict of interest.

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