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Proceedings of the American Mathematical Society

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

 

 

On a class of close-to-convex functions


Author: H. Silverman
Journal: Proc. Amer. Math. Soc. 36 (1972), 477-484
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1972-0313494-X
MathSciNet review: 0313494
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Abstract: We look at functions $ f(z)$ for which there correspond functions $ \phi (z)$ convex of order $ \alpha $ such that $ \operatorname{Re} \{ f'(z)/\phi '(z)\} \geqq \beta $. We examine the influence of the second coefficient of $ \phi (z)$ on this class. In particular, distortion, covering, and radius of convexity theorems are proved.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0313494-X
Keywords: Univalent, starlike, convex, close-to-convex, radius of convexity
Article copyright: © Copyright 1972 American Mathematical Society