On Zero Free Regions for Derivatives of a Polynomial

Abstract

Let P n denote the set of polynomials of the formstated the problem "Find the best constant C n such that p ′ (z) does not vanish in |z| < C n ". He also conjectured in the same paper that C n = 1 n . This problem was solved by Aziz and Zarger [1]. In this paper, we obtain the results which generalizes the results of Aziz and Zarger.