Inequalities for the polar derivative of a polynomial

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


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.


Polynomial Polar derivative Inequalities 

Mathematics Subject Classification

30A10 30C15 



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

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Forum D'Analystes, Chennai 2020

Authors and Affiliations

  1. 1.Department of MathematicsKashmir UniversitySrinagarIndia

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