On an extension of the concept of deficiency in the theory of meromorphic functions
Olli LEHTO (1953)
Mathematica Scandinavica
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Olli LEHTO (1953)
Mathematica Scandinavica
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Ilpo Laine, Gary G. Gundersen (1990)
Mathematica Scandinavica
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C.L. Childress, G.L. Csordas (1978)
Mathematica Scandinavica
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Ilpo Laine, Steven Bank (1977)
Mathematica Scandinavica
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Li Kam Shun, Chan Wai Leung (1992)
Mathematica Scandinavica
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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, 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.
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.
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.
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].
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.
S. K. Bajpai, T. J. S. Mehrok (1975)
Annales Polonici Mathematici
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Yang, Chung-Chun, Hua, Xinhou (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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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).
H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)
Annales Polonici Mathematici
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I. Lahiri (1989)
Matematički Vesnik
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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1977)
Annales Polonici Mathematici
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Henryka Siejka (1987)
Mathematica Scandinavica
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