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Proceedings of the American Mathematical Society

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

 

 

On bounds for the derivative of analytic functions


Author: Dorothy Browne Shaffer
Journal: Proc. Amer. Math. Soc. 37 (1973), 517-520
MSC: Primary 30A76
DOI: https://doi.org/10.1090/S0002-9939-1973-0310256-5
MathSciNet review: 0310256
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Abstract: Let $ g(z)$ be analytic and $ \vert g(z)\vert \leqq 1$ in $ \vert z\vert < 1;g(z) = \sum\nolimits_{k = p}^\infty {{a_k}{z^k},p \geqq 1} $, then a sharp upper bound is derived for $ \vert g'(z)\vert$. Let $ h(z)$ be analytic for $ \vert z\vert < 1,h(0) = 1,\operatorname{Re} h(z) > \alpha $ where $ 0 \leqq \alpha < 1$, then bounds for $ \vert h'(z)\vert$ are derived and sharpened for a function with missing terms.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0310256-5
Article copyright: © Copyright 1973 American Mathematical Society