The purpose of this paper is to deal with some uniqueness problems of entire functions or meromorphic functions concerning differential polynomials that share one value or fixed-points with finite weight. We obtain a number of theorems which generalize some results due to M.L. Fang & X.H. Hua, X.Y. Zhang & W.C. Lin, X.Y. Zhang & J.F. Chen and W.C. Lin.
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