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.

Uniqueness of meromorphic functions of differential polynomials sharing a small function with finite weight

Let f be a non-constant meromorphic function and {a=a(z)} ( {\not\equiv 0,\infty} ) a small function of f. Here, we obtain results similar to the results due to Indrajit Lahiri and Bipul Pal [Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. Korean Math. Soc. 54 2017, 3, 825–838] for a more general differential polynomial by introducing the concept of weighted sharing.

An entire function sharing fixed points with its linear differential polynomial

We study the uniqueness of entire functions, when they share a linear polynomial, in particular, fixed points, with their linear differential polynomials.