Complex Oscillation of Differential Polynomials Generated by Meromorphic Solutions of Linear Differential Equations
Benharrat Belaïdi (2011)
Publications de l'Institut Mathématique
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Benharrat Belaïdi (2011)
Publications de l'Institut Mathématique
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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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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)
Annales Polonici Mathematici
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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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Xu, Hong-Yan (2007)
International Journal of Mathematics and Mathematical Sciences
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Wang, Songmin, Gao, Zongsheng (2007)
Abstract and Applied Analysis
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Indrajit Lahiri (1999)
Annales Polonici Mathematici
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We prove a uniqueness theorem for meromorphic functions involving linear differential polynomials generated by them. As consequences of the main result we improve some previous results.
Meng, Chao (2007)
Applied Mathematics E-Notes [electronic only]
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Banerjee, Abhijit (2005)
International Journal of Mathematics and Mathematical Sciences
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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.
W. K. Hayman (1981)
Annales Polonici Mathematici
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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.
S. K. Singh, V. N. Kulkarni (1973)
Annales Polonici Mathematici
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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.
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.