Extension of Some Polynomial Inequalities to the Polar Derivative

Abstract

Let $p(z)$ be a polynomial of degree $n$ and ${D_\propto }p(z) = np(z) + (\propto - z)p'(z)$ denote the polar derivative of the polynomial $p(z)$ with respect to the point $\propto$. In this paper we obtain an inequality for the polar derivative of a polynomial which is an improvement of the result recently proved by Mir, Baba and Pukhta (2011) [Thai Journal of Mathematics, 9(2), 291--298].