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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Criteria for the extremality of the Koebe mapping


Authors: D. Bshouty and W. Hengartner
Journal: Proc. Amer. Math. Soc. 111 (1991), 403-411
MSC: Primary 30C50; Secondary 30C55
MathSciNet review: 1037204
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1037204-8
PII: S 0002-9939(1991)1037204-8
Article copyright: © Copyright 1991 American Mathematical Society