On the Order of Growth of Meromorphic Solutions of First-Order Differential Equations.
S.B. Bank, R.R Kaufman (1979)
Mathematische Annalen
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S.B. Bank, R.R Kaufman (1979)
Mathematische Annalen
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Tatsuo Suwa (1983)
Mathematische Annalen
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Ryutaro Horiuchi (1982)
Journal für die reine und angewandte Mathematik
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Reinhold Hübl (1994)
Mathematische Annalen
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Michael Schneider, Lucian Badescu (1996)
Mathematische Annalen
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Pascual Cutillas Ripoll (1986)
Mathematische Annalen
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S. K. Bajpai, T. J. S. Mehrok (1975)
Annales Polonici Mathematici
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I. Lahiri (1989)
Matematički Vesnik
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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.
H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1977)
Annales Polonici Mathematici
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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)
Annales Polonici Mathematici
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Stephen Scheinberg (1979)
Mathematische Annalen
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Kuldeep Singh Charak, Dominic Rochon, Narinder Sharma (2012)
Annales Polonici Mathematici
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We introduce the extended bicomplex plane 𝕋̅, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality...
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.
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.
Yuxian Chen, Zhaojun Wu (2012)
Annales Polonici Mathematici
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This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.
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.
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).