Abstract. In this paper we establish some refinements of Bernstein-type inequalities for rational functions with prescribed poles and restricted zeros, which generalizes the corresponding refinements of some polynomial inequalities due to Erdos-Lax, Turan and others. Generalization of a result of O'Hara and Rodriguez concerning self-inversive polynomials is also obtained for self-inversive rational functions.
1991 Mathematics Subject Classification. 26D07.
Key words and phrases. Inequalities in a complex domain, self-inversive rational function, polynomials, extremal problems.