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Proceedings of the American Mathematical Society

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

 
 

 

Distortion theorems for a special class of analytic functions


Author: Dorothy Browne Shaffer
Journal: Proc. Amer. Math. Soc. 39 (1973), 281-287
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1973-0315113-6
MathSciNet review: 0315113
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Abstract: Sharp bounds are derived for the derivative of analytic functions of class $ {P_\alpha }$ defined by the condition $ \vert p(z) - 1/2\alpha \vert \leqq 1/2\alpha ,0 \leqq \alpha \leqq 1,p(0) = 1$. These results are improved for the class of functions with missing terms. Application is made to the class of functions with derivative $ \in {P_\alpha }$ and the radius of convexity is determined for this class.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0315113-6
Article copyright: © Copyright 1973 American Mathematical Society

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