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 = {Chen , Junfan and Cai , Xiaohua}, 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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