Sujoy Majumder, Rajib Mandal (2018)
Archivum Mathematicum
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The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24].
Xiu-Qing Lin, Wei-Chuan Lin (2011)
Annales Polonici Mathematici
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This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].
Abhijit Banerjee, Molla Basir AHAMED (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper we improve, generalize and extend a number of recent results related to a problem of meromorphic function sharing a small function with its differential polynomial which are the continuation of a result earlier obtained by R. Brück.
Abhijit Banerjee (2006)
Annales Polonici Mathematici
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We study the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share the same 1-points. Our results improve results of Fang-Fang and Lin-Yi and supplement a recent result of Lahiri-Pal.
Yang, Chung-Chun, Hua, Xinhou (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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Indrajit Lahiri, Arindam Sarkar (2005)
Annales Polonici Mathematici
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We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.
Jun-Fan Chen (2017)
Open Mathematics
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We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
Indrajit Lahiri, Shyamali Dewan (2006)
Annales Polonici Mathematici
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We prove some normality criteria for a family of meromorphic functions and as an application we prove a value distribution theorem for a differential polynomial.
Wei-Ran Lü, Hong-Xun Yi (2003)
Annales Polonici Mathematici
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We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.
Abhijit Banerjee, Molla Basir Ahamed (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove the uniqueness of meromorphic functions sharing some three sets with finite weights.
Xiao-Min Li, Hong-Xun Yi (2010)
Annales Polonici Mathematici
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We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.
Xiao-Min Li, Hong-Xun Yi (2009)
Annales Polonici Mathematici
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We deal with a uniqueness theorem of two meromorphic functions that share three values with weights and also share a set consisting of two small meromorphic functions. Our results improve those by G. Brosch, I. Lahiri & P. Sahoo, T. C. Alzahary & H. X. Yi, P. Li & C. C. Yang, and others.
Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)
Open Mathematics
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In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
Pulak Sahoo (2012)
Mathematica Bohemica
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We study the uniqueness theorems of meromorphic functions concerning differential polynomials sharing a nonzero polynomial IM, and obtain two theorems which will supplement two recent results due to X. M. Li and L. Gao.
El Farissi, A., Belaidi, B. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Abhijit Banerjee, Bikash Chakraborty (2015)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
Hong Yan Xu, San Yang Liu (2017)
Open Mathematics
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The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).