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Volume 34, Issue 2
Some Normality Criteria for Families of Meromorphic Functions

Junfan Chen & Xiaohua Cai

Commun. Math. Res., 34 (2018), pp. 125-132.

Published online: 2019-12

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  • 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 $D$.

  • Keywords

meromorphic function, normal family, multiple value, shared value

  • AMS Subject Headings

30D45

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

junfanchen@163.com (Junfan Chen)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-125, author = {Junfan and Chen and junfanchen@163.com and 5492 and Department of Mathematics, Fujian Normal University, Fuzhou, 350117 and Junfan Chen and Xiaohua and Cai and and 5977 and Department of Mathematics, Fujian Normal University, Fuzhou, 350117 and Xiaohua Cai}, title = {Some Normality Criteria for Families of Meromorphic Functions}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {2}, pages = {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 $D$.

}, 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} }
TY - JOUR T1 - Some Normality Criteria for Families of Meromorphic Functions AU - Chen , Junfan AU - Cai , Xiaohua JO - Communications in Mathematical Research VL - 2 SP - 125 EP - 132 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.04 UR - https://global-sci.org/intro/article_detail/cmr/13518.html KW - meromorphic function, normal family, multiple value, shared value AB -

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 $D$.

Junfan Chen & Xiaohua Cai. (2019). Some Normality Criteria for Families of Meromorphic Functions. Communications in Mathematical Research . 34 (2). 125-132. doi:10.13447/j.1674-5647.2018.02.04
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