ON THE UNIQUENESS OF PRODUCT OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

Abstract

In this paper, we study the uniqueness of product of difference polynomials $f^{n}[\prod_{j=1}^{d}f(z+c_{j})^{s_{j}}]^{(k)}$ and $g^{n}[\prod_{j=1}^{d}g(z+c_{j})^{s_{j}}]^{(k)}$, which are sharing a fixed point $z$ and $f$, $g$ share $\infty$ IM. The result extends the previous results of Cao and Zhang\cite{9} into product of difference polynomials.