On the uniqueness of certain types of differential-difference polynomials

The purpose of the paper is to study the uniqueness problems of certain types of differential-difference polynomials sharing a small function or polynomial of certain degree under relaxed sharing hypothesis. We not only point out some gaps in the proof of the main results in [18] and [13], but also rectifying the errors, present our main results in a more compact way. In a nutshell, our results improve and generalize and rectify a recent result due to Zhang and Yi [18] and Liu and Yi [13]. Finally we indicate some questions for future research.