Normality Criteria of Meromorphic Functions Sharing a Meromorphic Function

Abstract:

      Let $\mathcal{F}$ be a family of meromorphic functions in $D$, and let $\psi(\neq 0)$ be a meromorphic function in $D$ all of whose poles are simple. Suppose that, for each $f\in\mathcal{F}$, $f\neq 0$ in $D$. If for each pair of functions $\{f,\,g\}\subset\mathcal{F}$, $f'$ and $g'$ share $\psi$ in $D$, then $\mathcal{F}$ is normal in $D$.