Note di Matematica. Some Results Concerning to Polar Derivative of Polynomials

Abstract

Let P(z) be a polynomial of degree n and for a complex number , let DP(z) = nP(z) + (alpha − z) P′(z) denote the polar derivative of the polynomial P(z) with respect to alpha .
In this paper we establish some Lr inequalities for the polar derivative of a polynomialwith restricted zeros. Our results not only generalizes some known polynomial inequalities, but also a variety of interesting results can be deduced from these by a fairly uniform procedure.