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Uniqueness of meromorphic functions and their differential polynomials. (English) Zbl 1318.30048

Summary: This paper studies uniqueness problem of two meromorphic functions whose differential polynomials share a small function. The results extend and improve a theorem given in [S. Wang and Z. Gao, Abstr. Appl. Anal. 2007, Article ID 60718, 6 p. (2007; Zbl 1152.30030)].

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Citations:

Zbl 1152.30030
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References:

[1] Fang, C.-Y., Fang, L.-M.: Uniqueness of meromorphic functions and differential polynomials. Comput. Math. Appl. 44, 607-617 (2002) · Zbl 1035.30018 · doi:10.1016/S0898-1221(02)00175-X
[2] Fang, M.L., Guo, H.: On unique range sets for meromorphic or entire functions. Acta. Math. Sin. 14, 569-576 (1998) · Zbl 0924.30038 · doi:10.1007/BF02580416
[3] Fang, M.L., Qiu, H.L.: Meromorphic functions that share fixed-points. J. Math. Anal. Appl. 268, 426-439 (2002) · Zbl 1030.30028 · doi:10.1006/jmaa.2000.7270
[4] Hayman, W.K.: Meromorphic Functions. Clarendon Press, Oxford (1964) · Zbl 0115.06203
[5] Wang, S.M., Gao, Z.S.: Meromorphic functions sharing a small function. Abstr. Appl. Anal. Art. 2007, 60718 (2007) · Zbl 1152.30030
[6] Yang, C.C.: On deficiencies of differential polynomials, π. Math. Z. 125, 107-112 (1972) · Zbl 0217.38402 · doi:10.1007/BF01110921
[7] Yang, C.C., Hua, X.: Uniqueness and value-sharing of meromorphic functions. Ann. Acad. Sci. Fenn. Math. 22, 395-406 (1997) · Zbl 0890.30019
[8] Yang, C.C., Yi, H.X.: Uniqueness Theory of Meromorphic Functions. Science Press/Kluwer, Beijing (2003) · Zbl 1070.30011 · doi:10.1007/978-94-017-3626-8
[9] Yang, L.: Value distribution theory and new research. Science Press, Beijing (1982) · Zbl 0633.30029
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