Uniqueness of Meromorphic Functions Concerning Sharing Two Small Functions with Their Derivatives

Linke Ma; Dan Liu; Mingliang Fang

doi:10.11948/20190115

2020 Volume 10 Issue 2

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Linke Ma, Dan Liu, Mingliang Fang. Uniqueness of Meromorphic Functions Concerning Sharing Two Small Functions with Their Derivatives[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 713-728. doi: 10.11948/20190115

Citation:

Linke Ma, Dan Liu, Mingliang Fang. Uniqueness of Meromorphic Functions Concerning Sharing Two Small Functions with Their Derivatives[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 713-728. doi: 10.11948/20190115

Uniqueness of Meromorphic Functions Concerning Sharing Two Small Functions with Their Derivatives

1.
Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China

Corresponding author: Email address:mlfang@scau.edu.cn(M. Fang)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11701188)

Abstract

Abstract

In this paper, we study the uniqueness of meromorphic functions that share two small functions with their derivatives. We prove the following result: Let $ f $ be a nonconstant meromorphic function such that $ \mathop {\overline{\lim}}\limits_{r\to\infty} \frac{\bar{N}(r, f)}{T(r, f)}<\frac{3}{128} $, and let $ a $, $ b $ be two distinct small functions of $ f $ with $ a\not\equiv\infty $ and $ b\not\equiv\infty $. If $ f $ and $ f' $ share $ a $ and $ b $ IM, then $ f\equiv f' $.
- Meromorphic functions /
- shared small functions /
- derivatives
MSC: 30D35

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References

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