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On uniqueness sets for areally mean $ p$-valent functions


Author: Enrique Villamor
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
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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

DOI: https://doi.org/10.1090/S0002-9939-1994-1211592-4
Keywords: Areally mean p-valent, logarithmic capacity
Article copyright: © Copyright 1994 American Mathematical Society

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