Research articles
ScienceAsia 52 (2023): 1-10 |doi:
10.2306/scienceasia1513-1874.2023.009
Uniqueness of meromorphic functions concerning derivatives
and fixed points
Jia Ana,b, Haiying Zhangb, Zhiying Hec, Mingliang Fanga,b,*
ABSTRACT: In this paper, we study the uniqueness of meromorphic function concerning derivatives and fixed points.
We mainly prove: Let n,k be two positive integers with n > 3k+8, and let f and g be two meromorphic functions all
whose zeros and poles have multiplicity at least n. If f (k) and g(k) share z CM, f and g share ? IM, then
(1) k=1,either f (z)= c1ecz2 , g(z)= c2e?cz2 , where c1,c2 and c are three constants satisfying 4c1c2c2 = ?1, or f ? g;
(2) k ?2, f ? g.
The result improves some results due to Fang-Qiu [J Math Anal Appl, 2002], Zhang [J Southeast Univ, 2004], Xu-L?u-Yi
[Comput Math Appl, 2010] and Zhang [Comput Math Appl, 2008].
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| a |
Department of Engineering, Shenzhen MSU-BIT University, Shenzhen 518172 China |
| b |
Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 China |
| c |
School of Arts and Sciences, Guangzhou Maritime University, Guangzhou 510725 China |
* Corresponding author, E-mail: mlfang@hdu.edu.cn
Received 9 Sep 2024, Accepted 0 0000
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