Growth of polynomials whose zeros are outside the unit circle

Abstract

In this paper we consider a polynomial P(z) having no zeros in the disk |z| < 1. We investigate the dependence of max|z|=R>1|P(z)| on max|z|=1|P(z)| and obtain a refinement of a famous result due to Ankeny and Rivilin. Our results not only generalize some polynomial inequalities but also refines a result of A. Aziz [1].