Some results on a question of Li, Yi and Li
DOI:
https://doi.org/10.24193/subbmath.2019.3.08Keywords:
Meromorphic function, shift operator, difference polynomial, uniqueness.Abstract
The purpose of this paper is to study the uniqueness problems of certain difference polynomials of meromorphic functions sharing a nonzero polynomial. The results of this paper improve and generalize some recent results due to Li, Yi and Li [11]. Some examples have been exhibited to show that some conditions used in the paper are sharp.
Mathematics Subject Classification (2010): 30D35.
References
Bergweiler, W., Eremenko, A., On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoam., 11(1995), 355-373.
Chen, Z.X., Huang, Z.B., Zheng, X.M., On properties of difference polynomials, Acta Math. Sci. Ser. B, 31(2011), no. 2, 627-633.
Chiang, Y.M., Feng, S.J., On the Nevanlinna characteristic f (z + η) and difference equations in complex plane, Ramanujan J., 16(2008), 105-129.
Chiang, Y.M., Feng, S.J., On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc., 361(7)(2009), 3767-3791.
Hayman, W.K., Picard values of meromorphic functions and their derivatives, Ann. Math., 70(1959), 9-42.
Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford, 1964.
Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Zhang, J.L., Value sharing results for shifts of meromorphic function and sufficient conditions for periodicity, J. Math. Anal. Appl., 355(2009), 352-363.
Lahiri, I., Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28(2001), 83-91.
Lahiri, I., Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theo. Appl., 46(2001), 241-253.
Laine, I., Yang, C.C., Value distribution of difference polynomials, Proc. Japan Acad. Ser. A, 83(2007), 148-151.
Li, X.M., Yi, M.X., Li, W.L., Value distribution of certain difference polynomials of meromorphic functions, Rocky Mountain J. Math., 44(2014), no. 2, 599-632.
Liu, K., Liu, X.L., Cao, T.B., Value distributions and uniqueness of difference polynomials, Adv. Diff. Equ., 2011 Article ID 234215, 12 pages.
Liu, K., Yang, L.Z., Value distribution of the difference operator, Arch. Math., 92(2009), 270-278.
Majumder, S., On the uniqueness of certain type of shift polynomial sharing a small function, Analele Univ. de Vest Timi¸soara, 55(2017), no. 1, 99-113.
Mues, E., U¨ber ein Problem von Hayman, Math Z., 164(1979), 239-259.
Qi, X.G., Yang, L.Z., Liu, K., Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl., 60(2010), 1739-1746.
Yamanoi, K., The second main theorem for small functions and related problems, Acta Math., 192(2004), 225-294.
Yang, C.C., On deficiencies of differential polynomials II, Math. Z., 125(1972), 107-112. [19] Yang, C.C., Yi, H.X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht-Boston-London, 2003.
Yi, H.X., Meromorphic functions that share one or two values, Complex Var. Theo. Appl., 28(1995), 1-11.
Zhang, J.L., Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367(2010), 401-408.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Studia Universitatis Babeș-Bolyai Mathematica
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.