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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conformality and semiconformality of a function holomorphic in the disk


Author: Shinji Yamashita
Journal: Trans. Amer. Math. Soc. 245 (1978), 119-138
MSC: Primary 30C55; Secondary 30D40, 30D45
MathSciNet review: 511402
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Abstract: Conformality and semiconformality at a boundary point, of a function f nonconstant and holomorphic in $ \left\vert z \right\vert < 1$ are local properties. Therefore one would suspect the requirement of such global conditions on f as f is univalent in $ \left\vert z \right\vert < 1$, or f is a member of a larger class which contains all univalent functions in $ \left\vert z \right\vert < 1$. We shall prove some extensions and new results without any assumption on f, or with a local assumption on f at most. Our methods are, for the most part, different from the ones in the classical cases. One of the main tools is Theorem 8 on the angular limits of the real part of a holomorphic function and its derivative.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0511402-X
PII: S 0002-9947(1978)0511402-X
Article copyright: © Copyright 1978 American Mathematical Society