In this paper we prove a sharp growth estimate for rational functions with prescribed poles and restricted zeros in the Chebyshev norm on the unit disk in the complex domain. In particular we extend a polynomial inequality due to Dubinin (2007) to rational functions which also improves a result of Govil and Mohapatra (1998).
Rational functions, polynomials, inequalities, growth estimates, Schwarz lemma
SHAH, LUBNA WALI
"On the growth of maximum modulus of rational functions with prescribed poles,"
Turkish Journal of Mathematics: Vol. 45:
1, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/2