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Proceedings of the American Mathematical Society

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

 

 

An extremal problem for functions with positive real part


Author: R. S. Gupta
Journal: Proc. Amer. Math. Soc. 33 (1972), 455-462
MSC: Primary 30A76
Erratum: Proc. Amer. Math. Soc. 42 (1974), 647.
MathSciNet review: 0293088
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Abstract: Let $ \mathcal{P}$ be the class of functions $ P(z)$, normalized so that $ P(0) = 1$ which are regular in $ \vert z\vert < 1$ and have positive real part there. We obtain the minimum (maximum) real part of $ {e^{i\alpha }}(zP'/P)$ for fixed $ \alpha $ and $ \vert z\vert,\alpha \in [0,2\pi ],\vert z\vert < 1$ and P running over the class $ \mathcal{P}$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293088-5
Keywords: Functions with positive real part, region of variability, variational formula
Article copyright: © Copyright 1972 American Mathematical Society