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

 

A unified approach to univalence criteria in the unit disc


Author: Martin Chuaqui
Journal: Proc. Amer. Math. Soc. 123 (1995), 441-453
MSC: Primary 30C35; Secondary 30C62
MathSciNet review: 1233965
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Abstract: From the recent injectivity criterion of Osgood and Stowe we recover many of the known univalence criteria in the unit disc D and derive as well new conditions on D and simply-connected domains. While the criteria of Epstein can be established in this fashion, we show how the 'diameter term' in the criterion of Osgood and Stowe gives a sharper form of a condition of Ahlfors. Finally, on simply-connected domains we find a sufficient condition for univalence that is the counterpart to a necessary one proved by Bergman and Schiffer.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1233965-7
PII: S 0002-9939(1995)1233965-7
Article copyright: © Copyright 1995 American Mathematical Society