arrow
Volume 35, Issue 3
Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values

Shengjiang Chen, Aizhu Xu & Xiuqing Lin

Commun. Math. Res., 35 (2019), pp. 283-288.

Published online: 2019-12

Export citation
  • Abstract

Let $E(a,\,f)$ be the set of $a$-points of a meromorphic function $f(z)$ counting multiplicities. We prove that if a transcendental meromorphic function $f(z)$ of hyper order strictly less than 1 and its $n$th exact difference $\Delta_c^nf(z)$ satisfy $E(1,\,f)=E(1,\,\Delta_c^nf)$, $E(0,\,f)\subset E(0,\,\Delta_c^nf)$ and $E(\infty,\,f)\supset E(\infty,\,\Delta_c^nf)$, then $\Delta_c^nf(z)\equiv f(z)$. This result improves a more recent theorem due to Gao et al. (Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their $n$th order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476018-0605-2) by using a simple method. 

  • Keywords

meromorphic function, exact difference, uniqueness, shared value

  • AMS Subject Headings

30D35, 39A10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ndsycsj@126.com (Shengjiang Chen)

xuaizhu@126.com (Aizhu Xu)

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-283, author = {Shengjiang and Chen and ndsycsj@126.com and 5500 and Department of Mathematics, Fujian Normal University, Fuzhou, 350007 and Shengjiang Chen and Aizhu and Xu and xuaizhu@126.com and 5499 and Department of Mathematics, Ningde Normal University, Ningde, Fujian, 352100 and Aizhu Xu and Xiuqing and Lin and and 6050 and Department of Mathematics, Ningde Normal University, Ningde, Fujian, 352100 and Xiuqing Lin}, title = {Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {283--288}, abstract = {

Let $E(a,\,f)$ be the set of $a$-points of a meromorphic function $f(z)$ counting multiplicities. We prove that if a transcendental meromorphic function $f(z)$ of hyper order strictly less than 1 and its $n$th exact difference $\Delta_c^nf(z)$ satisfy $E(1,\,f)=E(1,\,\Delta_c^nf)$, $E(0,\,f)\subset E(0,\,\Delta_c^nf)$ and $E(\infty,\,f)\supset E(\infty,\,\Delta_c^nf)$, then $\Delta_c^nf(z)\equiv f(z)$. This result improves a more recent theorem due to Gao et al. (Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their $n$th order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476018-0605-2) by using a simple method. 

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.09}, url = {http://global-sci.org/intro/article_detail/cmr/13533.html} }
TY - JOUR T1 - Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values AU - Chen , Shengjiang AU - Xu , Aizhu AU - Lin , Xiuqing JO - Communications in Mathematical Research VL - 3 SP - 283 EP - 288 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.03.09 UR - https://global-sci.org/intro/article_detail/cmr/13533.html KW - meromorphic function, exact difference, uniqueness, shared value AB -

Let $E(a,\,f)$ be the set of $a$-points of a meromorphic function $f(z)$ counting multiplicities. We prove that if a transcendental meromorphic function $f(z)$ of hyper order strictly less than 1 and its $n$th exact difference $\Delta_c^nf(z)$ satisfy $E(1,\,f)=E(1,\,\Delta_c^nf)$, $E(0,\,f)\subset E(0,\,\Delta_c^nf)$ and $E(\infty,\,f)\supset E(\infty,\,\Delta_c^nf)$, then $\Delta_c^nf(z)\equiv f(z)$. This result improves a more recent theorem due to Gao et al. (Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their $n$th order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476018-0605-2) by using a simple method. 

Sheng-jiang Chen, Ai-zhu Xu & Xiu-qing Lin. (2019). Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values. Communications in Mathematical Research . 35 (3). 283-288. doi:10.13447/j.1674-5647.2019.03.09
Copy to clipboard
The citation has been copied to your clipboard