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

• Main Authors: Xian Min Gui, Hong Yan Xu, Hua Wang
• Format: Article
• Language: English
• Published: AIMS Press 2020-09-01
• Series: AIMS Mathematics
• Subjects: small function; k-punctured; admissible meromorphic function; weighted shared
• Online Access: https://www.aimspress.com/article/10.3934/math.2020476/fulltext.html

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.