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On a maximal outer area problem for a class of meromorphic univalent fuctions

Published online by Cambridge University Press:  17 April 2009

Stephen M. Zemyan
Stephen M. Zemyan
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802.
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Abstract

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For 0 < p < 1, let Sp denote the class of functions f (z) which are meromorphic and univalent in the unit disk U, with the normalisations f (0) = 0, f′(0) = 1 and f (p) = ∞, and let Sp (a) denote subclass of Sp consisting of those functions in Sp whose residue at the pole in equal to a. In this paper, we determine, for values of the residue a in a certain disk Δp, the greatest possible outer area over all functions in the class Sp (a). We also determine additional information concerning extremal function if the reside a dose not lie in Δp.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 433 - 445
Copyright
Copyright © Australian Mathematical Society 1986

References

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