Uniqueness of entire functions concerning difference operator. (English) Zbl 1292.30017

Summary: We deal with a uniqueness question of entire functions sharing a nonzero value with their difference operators and obtain some results, which improve the results of X.-G. Qi et al. [Comput. Math. Appl. 60, No. 6, 1739–1746 (2010; Zbl 1202.30045)] and J.-L. Zhang et al. [Ann. Pol. Math. 102, No. 3, 213–221 (2011; Zbl 1236.39021].


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI


[1] Hayman, W. K., Meromorphic Functions (1964), Oxford, UK: Clarendon Press, Oxford, UK · Zbl 0115.06203
[2] Yang, L., Value Distribution Theory (1993), Berlin, Germany: Springer, Berlin, Germany · Zbl 0790.30018
[3] Yang, C.-C.; Yi, H.-X., Uniqueness Theory of Meromorphic Functions (2003), Dordrecht, The Netherlands: Kluwer Academic, Dordrecht, The Netherlands · Zbl 1070.30011 · doi:10.1007/978-94-017-3626-8
[4] Laine, I., Nevanlinna Theory and Complex Differential Equations. Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics, 15 (1993), Berlin, Germany: Walter de Gruyter & Co., Berlin, Germany · Zbl 0784.30002 · doi:10.1515/9783110863147
[5] Lahiri, I., Weighted sharing and uniqueness of meromorphic functions, Nagoya Mathematical Journal, 161, 193-206 (2001) · Zbl 0981.30023
[6] Qi, X.-G.; Yang, L.-Z.; Liu, K., Uniqueness and periodicity of meromorphic functions concerning the difference operator, Computers & Mathematics with Applications, 60, 6, 1739-1746 (2010) · Zbl 1202.30045 · doi:10.1016/j.camwa.2010.07.004
[7] Zhang, J. l.; Gao, Z. S.; Li, S., Distribution of zeros and shared values of difference operators, Annales Polonici Mathematici, 102, 3, 213-221 (2011) · Zbl 1236.39021 · doi:10.4064/ap102-3-2
[8] Chiang, Y.-M.; Feng, S.-J., On the Nevanlinna characteristic of \(f(z + \eta)\) and difference equations in the complex plane, Ramanujan Journal, 16, 1, 105-129 (2008) · Zbl 1152.30024 · doi:10.1007/s11139-007-9101-1
[9] Halburd, R. G.; Korhonen, R. J., Nevanlinna theory for the difference operator, Annales Academiæ Scientiarum Fennicæ. Mathematica, 31, 2, 463-478 (2006) · Zbl 1108.30022
[10] Li, P.; Yang, C.-C., Some further results on the unique range sets of meromorphic functions, Kodai Mathematical Journal, 18, 3, 437-450 (1995) · Zbl 0849.30025 · doi:10.2996/kmj/1138043482
[11] Yi, H. X., Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Variables. Theory and Application, 14, 1-4, 169-176 (1990) · Zbl 0701.30025 · doi:10.1080/17476939008814415
[12] Yi, H. X.; Yang, C. C., Uniqueness Theory of Meromorphic Functions (1995), Beijng, China: Science Press, Beijng, China
[13] Banerjee, A., Meromorphic functions sharing one value, International Journal of Mathematics and Mathematical Sciences, 2005, 22, 3587-3598 (2005) · Zbl 1093.30024 · doi:10.1155/IJMMS.2005.3587
[14] Lahiri, I.; Sarkar, A., Uniqueness of a meromorphic function and its derivative, Journal of Inequalities in Pure and Applied Mathematics, 5, 1, article 20 (2004) · Zbl 1056.30030
[15] Liu, K.; Liu, X. L.; Cao, T. B., Some results on zeros distributions and uniqueness of derivatives of difference polynomials
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.