zbMATH — the first resource for mathematics

Uniqueness theorems on meromorphic functions sharing one value. (English) Zbl 1142.30330
Summary: We study with a weighted sharing method the uniqueness problem of \([f^n(z)]^{(k)}\) and \([g^n(z)]^{(k)}\) sharing one value and obtain some results which extend the theorems given by M. Fang, S. Bhoosnurmath and S. Dyavanal et al.

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI
[1] Hayman, W.K., Meromorphic functions, (1964), Clarendon Press Oxford · Zbl 0115.06203
[2] Yi, H.X.; Yang, C.C., Uniqueness theory of meromorphic functions, (1995), Science Press Beijing · Zbl 0799.30019
[3] Hayman, W.K., Picard values of meromorphic functions and their derivatives, Ann. of math., 70, 9-24, (1959) · Zbl 0088.28505
[4] Cluine, J., On a result of Hayman, J. London math. soc., 42, 389-392, (1967) · Zbl 0169.40801
[5] Fang, M.L.; Hua, X.H., Entire functions that share one value, J. Nanjing univ. math., biquarterely, 13, 1, 44-48, (1996) · Zbl 0899.30022
[6] Yang, C.C.; Hua, X.H., Uniqueness and value-sharing of meromorphic functions, Ann. acad. sci. fenn. math., 22, 2, 395-406, (1997) · Zbl 0890.30019
[7] Hennekemper, G.; Hennekemper, W., Picard ausnahmewerte von ableitungen gewisser meromorpher funktion, Complex var., 5, 87-93, (1985) · Zbl 0537.30017
[8] Chen, H.H., Yosshida functions and Picard values of integral function and their derivatives, Bull. austral. math. soc., 54, 373-381, (1996)
[9] Bhoosnurmath, S.S.; Dyavanal, R.S., Uniqueness and value-sharing of meromorphic functions, Comput. math. appl., 53, 1191-1205, (2007) · Zbl 1170.30011
[10] Lahiri, I., Weighted value sharing and uniqueness of moromorphic functions, Complex var., 46, 241-253, (2001) · Zbl 1025.30027
[11] Lahiri, I.; Sarkar, A., Uniqueness of a moromorphic function and its derivative, J. inequal. pure appl. math., 5, 1, (2004), Art.20
[12] Zhang, Q.C., Meromorphic function that shares one small function with its derivative, J. inequal. pure appl. math., 6, 4, (2005), Art.116 · Zbl 1097.30033
[13] Frank, G., Eine vermutung von Hayman uber nullstellen meromorpher funktion, Math. Z., 149, 29-36, (1976) · Zbl 0312.30032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.