Unicity of mermorphic functions concerning shared functions with their difference
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1511-1524
Published online August 9, 2019
Printed November 30, 2019
Bingmao Deng, Mingliang Fang, Dan Liu
Guangdong University of Finance; South China Agricultural University; South China Agricultural University
Abstract : In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if $f(z)$ and $\Delta_c f(z)$ share $a(z), b(z), \infty$ CM, where $a(z), b(z) (\not \equiv \infty)$ are two distinct small functions of $f(z)$, then $f(z)\equiv \Delta_cf(z)$. The result improves the results due to Li et al.~(\cite{LXM}), Cui et al.~(\cite{CN}) and L\"{u} et al.~(\cite{LF}).
Keywords : uniqueness, meromorphic functions, difference operators
MSC numbers : Primary 30D35, 39A70
Supported by : This work was financially supported by NNSF of China (Grant No.11701188)
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