Inequalities for Rational Functions in the Complex plane

Abstract

In this paper, we establish inequalities for rational functions with prescribed poles and zeros inside or outside a disk of radius k. We find a generalized extension of the polynomial inequalities by Govil from 1973 and 1980 to rational functions. Additionally, we determine the relationship between the maximum modulus of a rational function on a circle of radius k (where k ≥ 1) and the unit circle. We also deduce refinements of certain inequalities by Li, Mohapatra, and Rodriguez from 1993.