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In this paper, with the aid of weighted sharing method we study the uniqueness problems of entire functions that share a nonconstant polynomial with weight two. The results of the paper improve and generalize some results due to [10] and [11].

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In this paper, we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a small function with finite weight. Our result generalizes and improves the recent results due to A. Banerjee and the present first author Sarajevo (Sarajevo J. Math. 8(20), 69-89, (2012)).

In this paper, with the aid of weighted value sharing we study the uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial with weight two. The result of the paper not only improves the results due to the present first author [Bull. Math. Anal. Appl., 2(2010), 106-118] and of Zhang and Xu [Comput. Math. Appl., 61(2011), 722-730], at the same time finds a possible answer of an open question posed by Zhang and Xu.