Far Eastern Mathematical Journal

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On a Class of Univalent Functions

V. N. Dubinin

2012, issue 2, P. 184–194

Abstract

In this paper we study the meromorphic univalent functions in the complex plane with radial slits. Covering and multipoint distortion theorems for such functions are proved. Some applications for rational functions are also given.

Keywords: meromorphic functions, univalent functions, distortion theorems, rational functions, condenser capacity, dissymmetrization

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References

[1] G. M. Goluzin, Geometricheskaia teoriia funktsii kompleksnogo peremennogo, Nauka, M., 1966. [2] M. A. Lavrent'ev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973. [3] M. Shiffer, “Nekotorye novye rezul'taty v teorii konformnykh otobrazhenii”, Prilozhenie k knige R. Kuranta, Printsip Dirikhle, konformnye otobrazheniia i minimal'nye poverkhnosti, IL, M., 1953. [4] V. N. Dubinin, Emkosti kondensatorov i simmetrizatsiia v geometricheskoi teorii funktsii kompleksnogo peremennogo, Dal'nauka, Vladivostok, 2009. [5] W. K. Hayman, Multivalent functions, Cambridge Univ. Press. Second ed., Cambridge, 1994. [6] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970.

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