In this paper, we study the zeros of difference polynomials of meromorphic functions of the forms
where is a nonzero polynomial of degree n, ( ) are distinct constants, , and is a small function of f. Our results of this paper are an improvement of the previous theorems given by Chen and Chen (Chinese Ann. Math., Ser. A 33(3):359-374, 2012) and Liu et al. (Appl. Math. J. Chin. Univ. Ser. B 27(1):94-104, 2012). In addition, we also investigate the uniqueness for difference polynomials of transcendental entire functions sharing one value and obtain some results which extend the recent theorem given by Liu et al. (Adv. Differ. Equ. 2011:234215, 2012).
MSC: 30D35, 39A10.