Uniqueness theorem for a meromorphic function and its exact difference
Bull. Korean Math. Soc.
Published online July 31, 2020
Shengjiang Chen and Aizhu Xu
Ningde Normal University
Abstract : Let $f(z)$ be a non-constant meromorphic function of hyper order strictly less than $1$, and let $c$ be a nonzero finite complex number such that $\Delta f(z)=f(z+c)-f(z)(\not\equiv0)$. We prove that if $f(z)$ and $\Delta f(z)$ share $0,\infty$ CM and $1$ IM, then $\Delta f(z)\equiv f(z)$. Our result generalizes and greatly improves the related results.
Keywords : Meromorphic function; exact difference; uniqueness; shared values.
MSC numbers : 30D35, 39A10
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