Some Inequalities for the Maximum Modulus of Rational Functions

Abstract

For a polynomial pz of degree n, it follows from the maximum modulus theorem that maxz=R≥1pz≤Rnmaxz=1pz. It was shown by Ankeny and Rivlin that if pz≠0 for z<1, then maxz=R≥1pz≤Rn+1/2maxz=1pz. In 1998, Govil and Mohapatra extended the above two inequalities to rational functions, and in this paper, we study the refinements of these results of Govil and Mohapatra.