## A unified approach to univalence criteria in the unit disc

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- by Martin Chuaqui PDF
- Proc. Amer. Math. Soc.
**123**(1995), 441-453 Request permission

## 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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## Additional Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 441-453 - MSC: Primary 30C35; Secondary 30C62
- DOI: https://doi.org/10.1090/S0002-9939-1995-1233965-7
- MathSciNet review: 1233965