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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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