Weighted sharing of a set and uniqueness of meromorphic functions with derivatives

Abstract

In this paper, we deal with meromorphic functions and its $k$th derivative. We consider a set of roots of unity, which shares the functions of the form ${(f^{n}P(f))}^{(k)}$ and ${(g^{n}P(g))}^{(k)}$ and obtain uniqueness results which improves the results of V. H. An and H. H. Khoai. Also, by introducing the concept of weighted sharing, we obtain analogous results from these authors.