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Keywords:
Uniqueness,Meromorphic functions; Sharing value; Differential polynomials.
Summary:
The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13].
References:
[1] Banerjee, A.: Meromorphic functions sharing one value. Int. J. Math. Math. Sci., 22, 2005, 3587-3598, DOI 10.1155/IJMMS.2005.3587 | MR 2205158 | Zbl 1093.30024
[2] Banerjee, A.: On uniqueness for nonlinear differential polynomials sharing the same 1-point. Ann. Polon. Math., 89, 3, 2006, 259-272, DOI 10.4064/ap89-3-3 | MR 2262553 | Zbl 1104.30018
[3] Dyavanal, R.S.: Uniqueness and value-sharing of differential polynomials of meromorphic functions. J. Math. Anal. Appl., 374, 1, 2011, 335-345, corrected republication of MR2672524. MR 2726211
[4] Fang, C.Y., Fang, M.L.: Uniqueness of meromorphic functions and differential polynomials. Comput. Math. Appl., 44, 5--6, 2002, 607-617, MR 1925805 | Zbl 1035.30018
[5] Fang, M.L., Hong, W.: A unicity theorem for entire functions concerning differential polynomials. Indian J. Pure Appl. Math., 32, 9, 2001, 1343-1348, MR 1875450 | Zbl 1005.30023
[6] Hayman, W.K.: Meromorphic functions. 1964, Oxford Mathematical Monographs Clarendon Press, MR 0164038 | Zbl 0115.06203
[7] Lahiri, I.: Uniqueness of meromorphic functions when two linear differential polynomials share the same 1-points. Ann. Polon. Math., 71, 2, 1999, 113-128, DOI 10.4064/ap-71-2-113-128 | MR 1703886 | Zbl 0938.30022
[8] Lahiri, I.: Linear differential polynomials sharing the same 1-points with weight two. Ann. Polon. Math., 79, 2, 2002, 157-170, DOI 10.4064/ap79-2-6 | MR 1957890
[9] Lahiri, I., Sahoo, P.: Uniqueness of meromorphic functions when two non-linear differential polynomials share a small function. Arch. Math., 44, 3, 2008, 201-210, MR 2462975
[10] Lin, W.Ch., Yi, H.X.: Uniqueness theorems for meromorphic function. Indian J. Pure Appl. Math., 35, 2, 2004, 121-132, MR 2040726 | Zbl 1056.30031
[11] Yang, Ch.Ch., Hua, X.: Uniqueness and value-sharing of meromorphic functions. Ann. Acad. Sci. Fenn. Math., 22, 2, 1997, 395-406, MR 1469799 | Zbl 0890.30019
[12] Yi, H.X.: Meromorphic functions that share one or two values. Complex Variables Theory Appl., 28, 1, 1995, 1-11, DOI 10.1080/17476939508814833 | MR 1700258 | Zbl 0841.30027
[13] Zhang, F., Wu, L.: Notes on the uniqueness of meromorphic functions concerning differential polynomials. J. Inequal. Appl, 2019, 2019, 1-14, MR 3923700
[14] Zhang, Q.: Meromorphic function that shares one small function with its derivative. JIPAM. J. Inequal. Pure Appl. Math., 6, 4, 2005, 13 pp, MR 2178297 | Zbl 1097.30033
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