Power of a meromorphic function that share a set with its derivative
DOI:
https://doi.org/10.24193/subbmath.2018.2.05Keywords:
Meromorphic function, weighted set sharing, uniqueness.Abstract
In this article, we deal with the problem of the uniqueness of the power of a meromorphic function with its derivative counterpart sharing a set and thus improve our recent result under some constraints.
Mathematics Subject Classification (2010): 30D35.
References
Alzahary, T.C., Meromorphic functions with weighted sharing of one set, Kyungpook Math. J., 47(2007), no. 1, 57-68.
Banerjee, A., Chakraborty, B., A new type of unique range set with deficient values, Afr. Mat., 26(2015), no. 7-8, 1561-1572.
Banerjee, A., Chakraborty, B., Uniqueness of the power of meromorphic functions with its differential polynomial sharing a set, Math. Morav., 20(2016), no. 2, 1-14.
Banerjee, A., Chakraborty, B., On the uniqueness of power of a meromorphic function sharing a set with its k-th derivative, J. Indian Math. Soc. (N.S.), 85(2018), no. 1-2, 1-15.
Chakraborty, B., Some aspects of uniqueness theory of entire and meromorphic functions, Ph.D. Thesis, arXiv: 1711.08808 [math.CV], 2017.
Hayman, W.K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
Lahiri, I., Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.
Lin, W.C., Yi, H.X., Uniqueness theorems for meromorphic functions that share three sets, Complex Var. Elliptic Equ., 48(2003), no. 4, 315-327.
Mokhon’ko, A.Z., On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Their Applications, Izd-vo Khar’kovsk, Un-ta, 14(1971), 83-87.
Mues, E., Steinmetz, N., Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math., 29(1979), no. 2-4, 195-206.
Rubel, L.A., Yang, C.C., Values shared by an entire function and its derivative, Complex Analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 101-103; Lecture Notes in Math., 599, Springer, Berlin, 1977.
Yang, L.Z., Zhang, J.L., Non-existence of meromorphic solutions of a Fermat type functional equation, Aequationes Math., 76(2008), no. 1-2, 140-150.
Zhang, J.L., Meromorphic functions sharing a small function with their derivatives, Kyungpook Math. J., 49(2009), no. 1, 143-154.
Zhang, J.L., Yang, L.Z., A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math., 34(2009), no. 1, 249-260.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
