Results on Uniqueness of Entire Functions Related to Difference Polynomial

In this paper, we deal with and improve one of the uniqueness results on two difference products of entire functions sharing one value by considering that the functions share the value zero, counting multiplicities. The research findings also include some IM-analogues of the theorems that we obtain, i.e. the nonzero value is allowed to be shared ignoring multiplicities. Meanwhile, we investigate the situation where the difference products share a nonzero polynomial instead, by confining its degree and generalize the previous concerning results. Moreover, we show by illustrating examples and a number of remarks that our results are best possible in certain senses.