Convex and starlike meromorphic functions

Abstract

In this paper we study meromorphic univalent functions with a simple pole at p which map the unit disk onto the exterior of convex sets or the exterior of starlike sets. A question raised by Libera and Livingston concerning the equality of two classes of starlike meromorphic univalent functions is answered. We show that the set of points omitted by the class of convex functions is { − p / ( 1 + p 2 ) } \{ - p/(1 + {p^2})\} . The coefficients of convex and starlike meromorphic functions are also studied.