Commun. Math. Res., 34 (2018), pp. 125-132.
Published online: 2019-12
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Let $k$ be a positive integer and $\cal F$ be a family of meromorphic functions in 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 finite complex 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 normal in $D$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.04}, url = {http://global-sci.org/intro/article_detail/cmr/13518.html} }Let $k$ be a positive integer and $\cal F$ be a family of meromorphic functions in 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 finite complex 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 normal in $D$.