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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convex and starlike meromorphic functions


Author: James Miller
Journal: Proc. Amer. Math. Soc. 80 (1980), 607-613
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1980-0587937-5
MathSciNet review: 587937
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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})\} $. The coefficients of convex and starlike meromorphic functions are also studied.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587937-5
Article copyright: © Copyright 1980 American Mathematical Society