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# Some results on uniqueness of an entire function with its shift difference

Dec 2022

In the paper, we have shown that every entire solution of the differentialdifference equation $\Delta_{\eta}^{m}f-Q_1=(\Delta_{\eta}^{k}f-Q_{2})e^{P}$satisfy hyper order of $f=$degree of $P$ and using this result we provedifferential difference counter part Br\"uck conjecture. Also we have proveddifferential difference counter part Br\"uck conjecture for the special case ofhyper order of $f<\frac{1}{2}$.

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