Further Results on Meromorphic Functions and Their $n$th Order Exact Differences with Three Shared Values

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. 

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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

Author Details

Shengjiang Chen

Aizhu Xu

Xiuqing Lin