The value distribution and uniqueness of one certain type of differential-difference polynomials

In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomials G(z)=(fn(fm(z)−1)∏j=1df(z+cj)uj)(k)−α(z),H(z)=(fn(f(z)−1)m∏j=1df(z+cj)uj)(k)−α(z), where f is transcendental entire function of finite order, cj(j=1,2,…,d), n,m,d, and vj(j=1,2,…,d) are integers, and obtain some theorems, which extended and improved many previous results.