Inequalities for the Polar Derivative of a Polynomial

摘要

Let P(z) be a polynomial of degree at most n. We consider an operator D_α which maps a polynomial P(z) into D α_P(z):= nP(z) + (α - z)P′(z) and prove results concerning the estimates of {pipe}D α_P(z){pipe} on the disk {pipe}z{pipe} = R ≥ 1, and thereby obtain extensions and generalizations of a number of well-known polynomial inequalities.