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Uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. (English) Zbl 1228.30024
Summary: We get two uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. The results in this paper extend the corresponding results given by M.-L. Fang [Comput. Math. Appl. 44, No. 5–6, 823–831 (2002; Zbl 1035.30017)]. Our reasoning in this paper will correct a defective reasoning in the proof of Theorem 4 in [S. S. Bhoosnurmath and R. S. Dyavanal, Comput. Math. Appl. 53, No. 8, 1191–1205 (2007; Zbl 1170.30011 )]. An example is provided to show that some conditions of the main results in this paper are necessary.

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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[1] Hayman, W.K., Meromorphic functions, (1964), The Clarendon Press Oxford · Zbl 0115.06203
[2] Laine, I., Nevanlinna theory and complex differential equations, (1993), Walter de Gruyter Berlin
[3] Yang, C.C.; Yi, H.X., Uniqueness theory of meromorphic functions, (2003), Kluwer Academic Publishers Dordrecht, Boston, London · Zbl 0799.30019
[4] Yang, L., Value distribution theory, (1993), Springer-Verlag Berlin, Heidelberg
[5] Lahiri, I., Weighted sharing of three values and uniqueness of meromorphic functions, Kodai math. J., 24, 421-435, (2001) · Zbl 0996.30020
[6] Lahiri, I., Uniqueness of meromorphic functions as governed by their differential polynomials, Yokohama math. J., 44, 147-156, (1997) · Zbl 0884.30023
[7] Fang, M.L., Uniqueness and value sharing of entire functions, Comput. math. appl., 44, 823-831, (2002) · Zbl 1035.30017
[8] Bhoosnurmath, S.S.; Dyavanal, R.S., Uniqueness and value sharing of meromorpphic functions, Comput. math. appl., 53, 1191-1205, (2007) · Zbl 1170.30011
[9] Yang, L., Normality for family of meromorphic functions, Sci. sinica ser. A, 29, 1263-1274, (1986) · Zbl 0629.30032
[10] Lahiri, I.; Sarkar, A., Uniqueness of a meromorphic function and its derivative, J. inequal. pure appl. math., 5, 1, (2004), Article 20 · Zbl 1056.30030
[11] Hayman, W.K.; Miles, J., On the growth of a meromorphic function and its derivatives, Complex variables theory appl., 12, 245-260, (1989) · Zbl 0643.30021
[12] Yi, H.X., Meromorphic functions that share three sets, Kodai math. J., 20, 22-32, (1997) · Zbl 0882.30019
[13] Zhang, Q.C., Meromorphic functions sharing three values, Indian J. pure appl. math., 30, 667-682, (1999) · Zbl 0934.30025
[14] A.Z. Mokhonko, On the Nevanlinna characteristics of some meromorphic functions, in: Theory of Functions, Functional Analysis and Their Applications, Izd-vo Khar’kovsk. Un-ta, vol.14, 1971, pp. 83-87.
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