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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The domain of univalence of certain families of rational functions


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 66 (1977), 85-90
MSC: Primary 30A32
MathSciNet review: 0584957
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Abstract: The Čakalov-Distler Theorem gives the domain of univalence for the family of all rational functions for which all the poles are simple, all the poles lie in a prescribed convex set, and all have positive residue. Here we extend this theorem to allow simple poles with negative residues. We include several open problems.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0584957-1
PII: S 0002-9939(1977)0584957-1
Keywords: Univalent functions, rational functions, domain of univalence, Čakalov-Distler Theorem
Article copyright: © Copyright 1977 American Mathematical Society