Some inequalities for maximum modules of polynomials

Abstract

A well-known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z)≠0 in |z|<1, then max|z|=R≥1|p(z)|≤(Rn+12)max|z|=1|p(z)|. In this paper we prove some generalizations and refinements of this result.