Generalizations of the area theorem for meromorphic univalent functions with nonzero pole. (English) Zbl 1369.30031
Summary: In this article, we consider meromorphic univalent functions \(f\) in the unit disc of the complex plane having a simple pole at \(z=\alpha\in (0,1)\) with nonzero residue \(b\) at \(z= \alpha\). P. N. Chichra [Proc. Camb. Philos. Soc. 66, 317–321 (1969; Zbl 0195.08903)] proved an area theorem for such functions. In this note, we generalize this theorem and prove an interesting consequence of this result.
MSC:
| 30D30 | Meromorphic functions of one complex variable (general theory) |
Keywords:
meromorphic fuctionsCitations:
Zbl 0195.08903References:
| [1] | P. N. Chichra, An area theorem for bounded univalent functions, Proc. Camb. Phil. Soc., 66 (1969), 317-321. · Zbl 0195.08903 · doi:10.1017/S030500410004500X |
| [2] | Pavlović, M., Introduction to function spaces on the disk (2004), Beograd · Zbl 1107.30001 |
| [3] | M. Pavlović and J. A. Peláez, Remarks on the area theorem in the theory of univalent functions, Proc. Amer. Math. Soc., 139(3) (2011), 909-916. · Zbl 1220.30031 · doi:10.1090/S0002-9939-2010-10333-7 |
| [4] | H. Prawitz, Über Mittelwerte analytischer Funktionen, Ark. Mat. Astr. Fys., 20 A (1927), 1-12. · JFM 53.0307.02 |
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