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

Hamilton, D. H.; Tuan, P. D.

doi:10.1090/S0002-9939-1978-0507331-3

An extremal problem for functions of positive real part with application to a radius of convexity problem
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by D. H. Hamilton and P. D. Tuan

Proc. Amer. Math. Soc. 72 (1978), 313-318

DOI: https://doi.org/10.1090/S0002-9939-1978-0507331-3

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Abstract:

The functional $\operatorname {Re} \{ zp’(z)/(p(z) + \beta + it)\} ,\beta > - 1,|z| \leqslant r,0 < r < 1$, 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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