LINEAR DIFFERENTIAL POLYNOMIALS WEIGHTED-SHARING A SET OF ROOTS OF UNITY

In this paper, we study the uniqueness of linear diFFerential polynomials of meromorphic functions when they share a set of roots of unity. Our results shall generalize recent results.

On uniqueness of two meromorphic functions when sharing three sets with finite weights

With the help of the notion of weighted sharing of sets, in this paper we have investigated on the question posed by Yi [17] regarding the uniqueness of meromorphic functions concerning three set sharing and obtained a result which significantly improved the recent results of Banerjee - Ahamed [3], Banerjee - Mukherjee [5] and Banerjee - Majumder [4] by removing the extra supposition as well as relaxing the nature of sharing. We have exhibited some examples to show the sharpness of the cardinalities of the set S 1 and the set S 2 considered in 1.1 and also to show that one can not obtained the same conclusions of the main results by considering any arbitrary sets.

Uniqueness of p(f) and P [f] concerning weakly weighted-sharing

In the year 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between “CM” and “IM”. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of a polynomial function p(f) of f and a homogeneous differential polynomial P [f] generated by f. Our results improve and generalizes the results due to Charak and Lal, S. Lin and W. Lin, and H-Y Xu and Y Hu.