Generalizations of Some Inequalities of the Polar Derivatives of Polynomials

TL;DR

This paper generalizes inequalities relating the modulus of polar derivatives of polynomials to the polynomials themselves, considering zeros inside and outside a disk and extremal coefficient positions.

Contribution

It introduces new generalized inequalities for polar derivatives of polynomials based on zero locations and coefficient extremal positions.

Findings

Derived generalized inequalities for polar derivatives

Considered zeros inside and outside a closed disk

Analyzed extremal coefficient positions

Abstract

The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the extremal coefficient position of the underlying polynomial.