Bull. Korean Math. Soc. 2020; 57(5): 1307-1317
Online first article July 31, 2020 Printed September 30, 2020
https://doi.org/10.4134/BKMS.b190998
Copyright © The Korean Mathematical Society.
Shengjiang Chen, Aizhu Xu
Ningde Normal University; Ningde Normal University
Let $f$ be a nonconstant meromorphic function of hyper order strictly less than $1$, and let $c$ be a nonzero finite complex number such that $f(z+c)\not\equiv f(z)$. We prove that if $\Delta_{c} f=f(z+c)-f(z)$ and $f$ share $0,\infty$ CM and $1$ IM, then $\Delta_{c} f= f$. Our result generalizes and greatly improves the related results.
Keywords: Meromorphic, exact difference, uniqueness, shared values
MSC numbers: Primary 30D35, 39A10
Supported by: This work was supported by the NNSF of China (No. 11801291), the Natural Science Foundation of Fujian (No. 2018J01424), the Training Program of Outstanding Youth Research Talents in Fujian (2018) and the project of Ningde Normal University (2019T01)
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