This paper investigates inequalities for rational functions with prescribed poles and zeros located inside or outside a disk of radius k. We extend classical polynomial inequalities due to Govil (1973, 1980) to the setting of rational functions. In particular, we establish a relationship between the maximum modulus of a rational function on the circle of radius k (where k ? 1) and on the unit circle. Our findings refine inequalities for rational functions previously obtained by Li, Mohapatra, and Rodriguez (1993), providing sharper bounds under certain conditions.
Idrees Qasim (2025) studied this question.