Results on a Conjecture of Chen and Yi
2021
In this paper, we prove that if a nonconstant finite order meromorphic function f and its n-th order difference operator $$\Delta ^n_{\eta }f$$
share $$a_1,$$
$$a_2,$$
$$a_3$$
CM, where n is a positive integer, $$\eta \ne 0$$
is a finite complex value, and $$a_1,$$
$$a_2,$$
$$a_3$$
are three distinct finite complex values, then $$f(z)=\Delta ^n_{\eta }f(z)$$
for each $$z\in \mathbb {C}.$$
The main results in this paper improve and extend many known results concerning a conjecture posed by Chen and Yi in 2013.
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