Criteria for the extremality of the Koebe mapping

Bshouty, D.; Hengartner, W.

doi:10.1090/S0002-9939-1991-1037204-8

Criteria for the extremality of the Koebe mapping
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by D. Bshouty and W. Hengartner PDF

Proc. Amer. Math. Soc. 111 (1991), 403-411 Request permission

Abstract:

A criterion is developed which gives a necessary condition on a real functional in order that the Koebe Mapping be extremal for this functional in the well known class $S$ of normalized univalent functions. This is applied to the coefficient problem of ${[f(z)]^\lambda },0 < \lambda < 1$ as well as to the problem of univalence of sections of the power series expansion of $f(z)$.

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