Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values
Year: 2019
Author: Shengjiang Chen, Aizhu Xu, Xiuqing Lin
Communications in Mathematical Research , Vol. 35 (2019), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2019.03.09
Communications in Mathematical Research , Vol. 35 (2019), Iss. 3 : pp. 283–288
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: meromorphic function exact difference uniqueness shared value