On the growth of maximum modulus of rational functions with prescribed poles

Authors: LUBNA WALI SHAH

Abstract: 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).

Keywords: Rational functions, polynomials, inequalities, growth estimates, Schwarz lemma

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