Some Normality Criteria for Families of Meromorphic Functions (Communications in Mathematical Research, 2019)
Let $k$ be a positive integer and $\cal F$ be a family of meromorphic functionsin a domain $D$ such that for each $f\in{\cal F}$, all poles of $f$ are of multiplicity at least 2,and all zeros of $f$ are of multiplicity at least $k+1$. Let $a$ and $b$ be two distinct finitecomplex numbers. If for each $f\in{\cal F}$, all zeros of $f^{(k)}-a$ are of multiplicity at least 2,and for each pair of functions $f,\,g\in{\cal F}$, $f^{(k)}$and $g^{(k)}$share $b$ in $D$, then $\cal F$ is normalin $D$.
Keywords: meromorphic function; normal family; multiple value; shared value