Inequalities for the polar derivative of a polynomial

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.

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Acknowledgements

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

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Correspondence to M. H. Gulzar.

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Gulzar, M.H., Zargar, B.A. & Akhter, R. Inequalities for the polar derivative of a polynomial. J Anal 28, 923–929 (2020). https://doi.org/10.1007/s41478-020-00222-4

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Keywords

  • Polynomial
  • Polar derivative
  • Inequalities

Mathematics Subject Classification

  • 30A10
  • 30C15