Some Inequalities Concerning the Polar Derivative of a Polynomial

Abdullah Mir, Bilal Dar

Abstract

In this paper, we consider the class of polynomials$P(z)=a_{n}z^{n}+\sum\limits_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}, 1\leq\mu\leq n$, having all zeros in $|z|\leq k,~k\leq 1$ and thereby establish several interesting estimates pertaining to the maximum modulus of the polar derivative of a polynomial $P(z)$. Our results not only generalize and refine some known polynomial inequalities, but also a variety of interesting results can be deduced from these by a fairly uniform procedure.