EXTREME-POINTS AND MINIMAL OUTER AREA PROBLEM FOR MEROMORPHIC UNIVALENT-FUNCTIONS

For 0 < p < 1, let S-p denote the class of functions f(z) meromorphic univalent in the unit disk D with the normalization f(0)= 0, f'(0)= 1, and f(p)= ca. Let S-p(a) be the subclass of S-p with the fixed residu e a. In this note we determine the extreme points of the class S-p(a). As an application, we solve the problem of minimizing the outer area over S-p(a), which was posed by S. Zemyan (J. Analyse Math. 39, 1981, 11-23). (C) 1998 Academic Press.