Bulletin of the
Korean Mathematical Society BKMS

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)