Extreme Points and Minimal Outer Area Problem for Meromorphic Univalent Functions

For 0-p-1, let Sp denote the class of functions f z. meromorphic univalent in the unit disk D with the normalization f 0.s0, f 9 0.s1, and f p.s`. Let Sp a. be the subclass of Spwith the fixed residue a. In this note we determine the extreme points of the class Sp a.. As an application, we solve the problem of minimizing the outer area over Sp a., which was posed by S. Zemyan J. Analyse Math. 39, 1981, 11]23..