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On bounded univalent functions that omit two given values

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Betsakos D.

Colloquium Mathematicum

1999

tom 80

nr 2

253-258

Let a,b ∈ {z: 0<|z|<1} and let S(a,b) be the class of all univalent functions f that map the unit disk 𝔻 into 𝔻\{a,b} with f(0)=0. We study the problem of maximizing |f'(0)| among all f ∈ S(a,b). Using the method of extremal metric we show that there exists a unique extremal function which maps 𝔻 onto a simply connnected domain $D_0$ bounded by the union of the closures of the critical trajectories of a certain quadratic differential. If a<0

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1 Colloquium Mathematicum

1 Betsakos D.

1 1999

Wyniki wyszukiwania

On bounded univalent functions that omit two given values