Uniqueness theorem for a meromorphic function and its exact difference
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1307-1317
Published online September 30, 2020
Shengjiang Chen, Aizhu Xu
Ningde Normal University; Ningde Normal University
Abstract : 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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