Bernstein-Type Inequalities for the Polar Derivative of a Polynomial

Abstract

Inequalities of Markov and Bernstein were the starting point of considerable literature in polynomial approximation theory. The problem of obtaining exact new bonds, the improvements and the extensions of some old results for the maximum modulus of P'(z) on the unit disk |z|=1 are still of considerable interest. In view of this fact and many unsettled problems, the analytic theory of polynomials continues to be an active field of research. The aim of this dissertation to present a survey of certain results concerning the estimates for the maximum modulus of the polar derivative of a polynomial on the unit disk with or without restriction on the zeroes of a polynomial