Normal criterion and shared values by derivatives of meromorphic functions

Abstract

Let $\mathscr{F}$ be a family of meromorphic functions in a plane domain $D$. If for every function $f\in\mathscr{F}$, all of whose zeros have,at least,multiplicity $l$ and poles have, at least,multiplicity $p$, and for each pair functions $f$ and $g$ in $\mathscr{F}$, $f^{(k)}$ and $g^{(k)}$ share 1 in $D$, where $k,l,$ and $p$ are three positive integer satisfying $\frac{k+1}{l}+\frac{1}{p}\leq 1$, then $\mathscr{F}$ is normal.