An extremal problem for functions with positive real part

Gupta, R. S.

doi:10.1090/S0002-9939-1972-0293088-5

An extremal problem for functions with positive real part
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by R. S. Gupta

Proc. Amer. Math. Soc. 33 (1972), 455-462

DOI: https://doi.org/10.1090/S0002-9939-1972-0293088-5

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Erratum: Proc. Amer. Math. Soc. 42 (1974), 647.

Abstract:

Let $\mathcal {P}$ be the class of functions $P(z)$, normalized so that $P(0) = 1$ which are regular in $|z| < 1$ and have positive real part there. We obtain the minimum (maximum) real part of ${e^{i\alpha }}(zP’/P)$ for fixed $\alpha$ and $|z|,\alpha \in [0,2\pi ],|z| < 1$ and P running over the class $\mathcal {P}$.

References

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