arrow
Volume 32, Issue 1
Normality Criteria of Meromorphic Functions

Qiong Wang, Wenjun Yuan, Wei Chen & Honggen Tian

Commun. Math. Res., 32 (2016), pp. 88-96.

Published online: 2021-03

Export citation
  • Abstract

In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D, m, n, k$ and $d$ be four positive integers satisfying $m ≥ n + 2$ and $d ≥ \frac{k + 1}{m − n − 1}$, and $a(≠0), b$ be two finite constants. Suppose that every $f ∈ \mathcal{F}$ has all its zeros and poles of multiplicity at least $k$ and $d$, respectively. If $(f^n)^{(k)}−af^m$ and $(g^n)^{(k)}−ag^m$ share the value $b$ for every pair of functions $(f, g)$ of $\mathcal{F}$, then $\mathcal{F}$ is normal in $D$. Our results improve the related theorems of Schwick (Schwick W. Normality criteria for families of meromorphic function. $J$. $Anal$. $Math$., 1989, 52: 241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. $J$. $Math$. $Anal$. $Appl$., 2009, 354: 421–425).

  • Keywords

meromorphic function, shared value, normal criterion.

  • AMS Subject Headings

30D30, 30D45

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-32-88, author = {Qiong and Wang and and 18466 and and Qiong Wang and Wenjun and Yuan and and 18467 and and Wenjun Yuan and Wei and Chen and and 19313 and and Wei Chen and Honggen and Tian and and 18815 and and Honggen Tian}, title = {Normality Criteria of Meromorphic Functions}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {1}, pages = {88--96}, abstract = {

In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D, m, n, k$ and $d$ be four positive integers satisfying $m ≥ n + 2$ and $d ≥ \frac{k + 1}{m − n − 1}$, and $a(≠0), b$ be two finite constants. Suppose that every $f ∈ \mathcal{F}$ has all its zeros and poles of multiplicity at least $k$ and $d$, respectively. If $(f^n)^{(k)}−af^m$ and $(g^n)^{(k)}−ag^m$ share the value $b$ for every pair of functions $(f, g)$ of $\mathcal{F}$, then $\mathcal{F}$ is normal in $D$. Our results improve the related theorems of Schwick (Schwick W. Normality criteria for families of meromorphic function. $J$. $Anal$. $Math$., 1989, 52: 241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. $J$. $Math$. $Anal$. $Appl$., 2009, 354: 421–425).

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.01.07}, url = {http://global-sci.org/intro/article_detail/cmr/18666.html} }
TY - JOUR T1 - Normality Criteria of Meromorphic Functions AU - Wang , Qiong AU - Yuan , Wenjun AU - Chen , Wei AU - Tian , Honggen JO - Communications in Mathematical Research VL - 1 SP - 88 EP - 96 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.01.07 UR - https://global-sci.org/intro/article_detail/cmr/18666.html KW - meromorphic function, shared value, normal criterion. AB -

In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D, m, n, k$ and $d$ be four positive integers satisfying $m ≥ n + 2$ and $d ≥ \frac{k + 1}{m − n − 1}$, and $a(≠0), b$ be two finite constants. Suppose that every $f ∈ \mathcal{F}$ has all its zeros and poles of multiplicity at least $k$ and $d$, respectively. If $(f^n)^{(k)}−af^m$ and $(g^n)^{(k)}−ag^m$ share the value $b$ for every pair of functions $(f, g)$ of $\mathcal{F}$, then $\mathcal{F}$ is normal in $D$. Our results improve the related theorems of Schwick (Schwick W. Normality criteria for families of meromorphic function. $J$. $Anal$. $Math$., 1989, 52: 241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. $J$. $Math$. $Anal$. $Appl$., 2009, 354: 421–425).

Qiong Wang, Wenjun Yuan, Wei Chen & Honggen Tian. (2021). Normality Criteria of Meromorphic Functions. Communications in Mathematical Research . 32 (1). 88-96. doi:10.13447/j.1674-5647.2016.01.07
Copy to clipboard
The citation has been copied to your clipboard