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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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On uniqueness sets for areally mean $p$-valent functions
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by Enrique Villamor PDF
Proc. Amer. Math. Soc. 122 (1994), 1143-1151 Request permission

Abstract:

We study the sets of uniqueness of areally mean p-valent functions in the unit disc. Namely, if $f(z)$ is in this class and has the same angular limit in a set E on the boundary of the unit disc, we prove that if p is small compared to the size of E then $f(z)$ is constant. We then construct an areally mean p-valent function which shows that some condition on the size of the set E must be imposed.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 1143-1151
  • MSC: Primary 30C45
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1211592-4
  • MathSciNet review: 1211592