Uniqueness Of Meromorphic Functions Concerning The Difference Polynomials

In this paper, we investigate the uniqueness problems of difference polyno-mialys of meromorphic functions that share a non-constant rational function. We generalize some recent results in Liu et al.(2011)[8]. We obtain some results as follows.Theorem2.1. Let f, g be transcendental meromorphic functions with finite order. Suppose that c is a nonzero constant and n∈N. If n≥14, fnf(z+c) and gng(z+c) share a(z) CM, where a(z) is a non-constant rational function, and satisfies T(r.a)<≤n-2/2logr+O(1), then f=hg, where hn+1=1, and h is a constant.Theorem2.2. Under the conditions of Theorem2.1, if n≥26, fnf(z+c) and gng(z+c) share a(z) IM, where a(z) is a non-constant rational function and satisfies T(r,a)≤n-2/2logr+O(1), then f=dg, where dn+1=1, and d is a constant.