Further Results about the Normal Family of Meromorphic Functions and Shared Sets

Let $\mathcal{F}$ be a family of meromorphic functions in a domain D, and let $k$, $n({\geq}2)$ be two positive integers, and let $S=\{a_1,a_2,{\ldots},a_n\}$, where $a_1$, $a_2$, ${\ldots}$, $a_n$ are distinct finite complex numbers. If for each $f{\in}\mathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then$\mathcal{F}$ is normal in $D$.