Uniqueness of meromorphic functions sharing small functions in the <i>k</i>-punctured complex plane

Abstract

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.