Entire functions sharing one or two finite values CM with their shifts or difference operators (Q652224)

For a meromorphic function \(f(z)\) and a nonzero complex constant \(\eta\) consider the difference operators \[ \Delta_{\eta}f(z)=f(z+\eta)-f(z)\quad \text{and}\quad\Delta^{n}_{\eta}f(z)=\Delta^{n-1}_{\eta}(\Delta_{\eta}f(z)), \] where \(n=2,3, \dots\). Under certain assumptions, the authors consider the uniqueness of \(f(z)\) and \(f(z+\eta)\) (or \(f(z)\) and \(\Delta^{n}_{\eta}f(z)\)) sharing one or two finite values CM. Furthermore, the difference analogues of the Brück conjecture are also obtained.