Properties of q-shift difference-differential polynomials of meromorphic functions

In this paper, we deal with the zeros of the q-shift difference-differential polynomials [P(f)∏j=1df(qjz+cj)sj](k)−α(z) and (P(f)∏j=1d[f(qjz+cj)−f(z)]sj)(k)−α(z), where P(f) is a nonzero polynomial of degree n, qj,cj∈C∖{0} (j=1,…,d) are constants, n,d,sj(j=1,…,d)∈N+ and α(z) is a small function of f. The results of this paper are an extension of the previous theorems given by Chen and Chen and Qi. We also investigate the value sharing for q-shift difference polynomials of entire functions and obtain some results which extend the recent theorem given by Liu, Liu and Cao.