ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30 Complex Analysis Ahuja, Om P., Division of Mathematics, National Institute of Education, Nanyang Technolgoical University, 469 Bukit Timah Road, Singapore 259756, Republic of Singapore, and Nunokawa, M., Department of Mathematics, University of Gunma, Aramaki, Maebashi, 371 Japan On Meromorphic Starlike and Convex Functions It is well known that Marx and Strohhacker (in 1932/1933) proved if f is a convex univalent function, then f is a starlike univalent function of order 1/2. Subsequently, Macgregor [J. London. Math. Soc., 9 (1975), 530–536] and Wilken and Feng [J. London. Math. Soc., 21 (1980), 287–290] showed that if f is a convex univalent function of order α(0 ≤ α < 1), then f is a starlike univalent function of order β = β(α) for some β. In this paper we show that the meromorphic convex univalent functions and meromorphic starlike univalent functions do not have the same relationships as those between the convex univalent functions and starlike univalent functions.