Two meromorphic functions sharing five small functions in the sense of $\overline E_{k)}(\beta,f)=\overline E_{k)}(\beta,g)$

Abstract

In this paper, we proved a result that if two meromorphic functions $f(z)$ and $g(z)$ share five small functions $a_j(z) \ \ (j=1,\ldots,5)$ in the sense of $\overline{E}_{k)}(a_j,f)=\overline{E}_{k)}(a_j,g)$, $(j=1,\ldots,5)$ ($k\geq 22$), then we have $f(z)\equiv g(z)$.