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Proceedings of the American Mathematical Society

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An extremal problem for functions of positive real part with application to a radius of convexity problem


Authors: D. H. Hamilton and P. D. Tuan
Journal: Proc. Amer. Math. Soc. 72 (1978), 313-318
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1978-0507331-3
MathSciNet review: 507331
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Abstract: The functional $ \operatorname{Re} \{ zp'(z)/(p(z) + \beta + it)\} ,\beta > - 1,\vert z\vert \leqslant r,0 < r < 1$, is minimized for all real t over the class of functions of positive real part. The result is applied to obtain the radius of convexity for a family of regular functions.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0507331-3
Keywords: Extremal problem, radius of convexity, functions of positive real part
Article copyright: © Copyright 1978 American Mathematical Society

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