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 Unicity of mermorphic functions concerning shared functions with their difference Bull. Korean Math. Soc.Published online August 9, 2019 Bingmao Deng, Mingliang Fang, and Dan Liu Institute of Applied Mathematics, 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 improve the results due to Li et al (Bull. Korean Math. Soc., 2015), Cui et al (J. Diff. Equ. Appl., 2016) and L\"{u} et al (Comput. Methods Funct. Theory, 2017). Keywords : Uniqueness, meromorphic functions, difference operators MSC numbers : 30D35; 39A70 Full-Text :