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On the multiple values and uniqueness of meromorphic functions on annuli. (English) Zbl 1189.30065

Summary: The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions on annuli. We prove a general theorem on the multiple values and uniqueness of meromorphic functions on annuli, from which an analog of Nevanlinna’s famous five-value theorem is proposed.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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[1] Hayman, W., Meromorphic functions, (1964), Clarendon Press Oxford · Zbl 0115.06203
[2] Yang, L., Value distribution theory, (1993), Springer-Verlag Berlin, Science Press, Beijing, 1982
[3] Nevanlinna, R., Eindentig keitssätze in der theorie der meromorphen funktionen, Acta. math., 48, 367-391, (1926) · JFM 52.0323.03
[4] Yi, H.-X.; Yang, C.-C., Uniqueness theory of meromorphic functions, (1995), Science Press, Kluwer, 2003
[5] Banerjee, A., Weighted sharing of a small function by a meromorphic function and its derivative, Comput. math. appl., 53, 1750-1761, (2007) · Zbl 1152.30321
[6] Bhoosnurmath, S.S.; Dyavanal, R.S., Uniqueness and value-sharing of meromorphic functions, Comput. math. appl., 53, 1191-1205, (2007) · Zbl 1170.30011
[7] Zhang, X.-Y.; Chen, J.-F.; Lin, W.-C., Entire or meromorphic functions sharing one value, Comput. math. appl., 56, 1876-1883, (2008) · Zbl 1152.30326
[8] Axler, S., Harmonic functions from a complex analysis viewpoint, Amer. math. monthly, 93, 246-258, (1986) · Zbl 0604.31001
[9] Khrystiyanyn, A.Ya.; Kondratyuk, A.A., On the Nevanlinna theory for meromorphic functions on annuli, I, mat. stud., 23, 1, 19-30, (2005) · Zbl 1066.30036
[10] Khrystiyanyn, A.Ya.; Kondratyuk, A.A., On the Nevanlinna theory for meromorphic functions on annuli. II, Mat. stud., 24, 2, 57-68, (2005) · Zbl 1092.30048
[11] A.A. Kondratyuk, I. Laine, Meromorphic functions in multiply connected domains, in: Laine, Ilpo (Ed.), Fourier Series Methods in Complex Analysis, Proceedings of the workshop, Mekrijärvi, Finland, July 24-29, 2005. Joensuu: University of Joensuu, Department of Mathematics (ISBN 952-458-888-9/pbk). Report series. Department of mathematics, University of Joensuu 10, 9-111, 2006 · Zbl 1144.30013
[12] Yi, H.-X., The multiple values of meromorphic functions and uniqueness, Chinese ann. math. ser. A, 10, 4, 421-427, (1989) · Zbl 0702.30030
[13] Li, Y.-H.; Qiao, J.-Y., On the uniqueness of meromorphic functions concerning small functions, Sci. China ser. A, 29, 891-900, (1999)
[14] Yao, W.-H., Two meromorphic functions sharing five small functions in the sense \(\overline{E}_k(\beta, f) = \overline{E}_k(\beta, g)\), Nagoya math. J., 167, 35-54, (2002) · Zbl 1032.30022
[15] Yi, H.-X., On one problem of uniqueness of meromorphic functions concerning small functions, Pro. amer. math. soc., 130, 1689-1697, (2001) · Zbl 1049.30022
[16] Thai, D.D.; Tan, T.V., Meromorphic functions sharing small functions as targets, Internat. J. math., 16, 4, 437-451, (2005) · Zbl 1080.30029
[17] Cao, T.-B.; Yi, H.-X., On the multiple values and uniqueness of meromorphic functions sharing small functions as targets, Bull. Korean math. soc., 44, 4, 631-640, (2007) · Zbl 1134.30020
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