Year: 2018
Author: Junfan Chen, Xiaohua Cai
Communications in Mathematical Research , Vol. 34 (2018), Iss. 2 : pp. 125–132
Abstract
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 $D$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2018.02.04
Communications in Mathematical Research , Vol. 34 (2018), Iss. 2 : pp. 125–132
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: meromorphic function normal family multiple value shared value