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Proceedings of the American Mathematical Society

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

 

 

The derivative of Bazilevič functions


Authors: R. R. London and D. K. Thomas
Journal: Proc. Amer. Math. Soc. 104 (1988), 235-238
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1988-0958074-X
Corrigendum: Proc. Amer. Math. Soc. 109 (1990), null.
MathSciNet review: 958074
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Abstract: For $ \alpha {\text{ > }}0$, let $ {B_1}(\alpha )$ be the class of normalised analytic functions $ f$ defined in the open unit disc $ D$ such that $ {\text{Re(}}f(z)/z{{\text{)}}^{\alpha - 1}}f'(z){\text{ > }}0$ for $ z \in D$. Sharp upper and lower bounds are obtained for $ \left\vert {zf'(z)/f(z)} \right\vert$ when $ f \in {B_1}(\alpha )$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0958074-X
Article copyright: © Copyright 1988 American Mathematical Society