Inequalities for the Polar Derivative of a Polynomial

TL;DR

This paper presents new inequalities related to the maximum modulus of the polar derivative of polynomials with zeros restricted to certain regions, extending previous results in polynomial growth and derivative bounds.

Contribution

It introduces generalized and refined inequalities for the polar derivative of polynomials with restricted zeros, building upon prior foundational work.

Findings

New bounds for the maximum modulus of the polar derivative

Generalizations of existing inequalities for polynomial derivatives

Refinements improving previous estimates in polynomial analysis

Abstract

In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J. Pure Appl. Math. 28 (1997) 1413--1419] and Gardner, Govil and Weems [Some result concerning rate of growth of polynomials, East J. Apporox. 10(2004) 301--312].