Zygmund's type inequality to the polar derivative of a polynomial

TL;DR

This paper extends Zygmund's inequality to the polar derivative of polynomials and improves recent related results, enhancing the understanding of polynomial inequalities with restricted zeros.

Contribution

It introduces a new inequality for the polar derivative of polynomials, generalizing Zygmund's inequality and improving prior bounds.

Findings

Extended Zygmund's inequality to polar derivatives

Improved bounds for polynomials with restricted zeros

Enhanced understanding of polynomial derivative inequalities

Abstract

In this paper we improve a result recently proved by Irshad et al. [On the Inequalities Concerning to the Polar Derivative of a Polynomial with Restricted Zeroes, Thai Journal of Mathematics, 2014 (Article in Press)] and also extend Zygmund's inequality to the polar derivative of a polynomial.