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AIMS Mathematics

2020, Volume 5, Issue 6: 7438-7457. doi: 10.3934/math.2020476
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Research article

Uniqueness of meromorphic functions sharing small functions in the k-punctured complex plane

  • 1.
    School of Science, Jiangxi University of Science and Technology, Ganzhou, Jiangxi, 341000, P. R. China
  • 2.
    Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, P. R. China
  • Received: 16 June 2020 Accepted: 14 September 2020 Published: 21 September 2020

  • MSC : 30D30, 30D35

  • The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j, l;f) = \widetilde{E}_\Omega(\alpha_j, l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j = 1, 2, \ldots, 5)$ are five distinct small functions with respect to $f$ and $g$. Our results are extension and improvement of previous theorems given by Ge and Wu, Cao and Yi.

    Citation: Xian Min Gui, Hong Yan Xu, Hua Wang. Uniqueness of meromorphic functions sharing small functions in the k-punctured complex plane[J]. AIMS Mathematics, 2020, 5(6): 7438-7457. doi: 10.3934/math.2020476

    Related Papers:

  • The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j, l;f) = \widetilde{E}_\Omega(\alpha_j, l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j = 1, 2, \ldots, 5)$ are five distinct small functions with respect to $f$ and $g$. Our results are extension and improvement of previous theorems given by Ge and Wu, Cao and Yi.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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