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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)Open image in new window and (P(f)∏j=1d[f(qjz+cj)−f(z)]sj)(k)−α(z)Open image in new window, where P(f)Open image in new window is a nonzero polynomial of degree n, qj,cj∈C∖{0}Open image in new window (j=1,…,dOpen image in new window) are constants, n,d,sj(j=1,…,d)∈N+Open image in new window and α(z)Open image in new window 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.

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