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In the paper we study the uniqueness problems of meromorphic functions whose certain nonlinear differential polynomials share certain value or fixed point with finite weight and obtain two theorems which improve two recent results due to S.S. Bhoosnurmath and S.R. Kabbur [Tamkang J. Math., 44, 11-22, Spring 2013]

Weighted sharing and uniqueness of memorphic functions with regard to multiplicity