In this paper, we deal with the value distribution of difference products of entire functions, and present some result on two difference products of entire functions sharing one value with the same multiplicities. The research findings also include an analogue for shift of a well-known conjecture by Brück. Our theorems improve the results of I. Value distribution of the difference operator, Arch. Math. 92 (2009) 270-278], and J. Heittokangas et al. [J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J.L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009) 352-363]. Moreover, we show by illustrating a number of examples that our results are best possible in certain senses.Published by Elsevier Inc.

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In this paper, we introduce the definition of weakly weighted-sharing which is between ''CM'' and ''IM''. Using the notion of weakly weighted-sharing, we study the uniqueness problems on meromorphic function and its kth order derivative f ðkÞ satisfying certain sharing set properties. As consequences, we are able to answer questions posed by Kit-wing Yu, which were also studied by I. Lahiri and A. Sarkar, L. P. Liu and Y. X. Gu. Our results sharpen the above results.

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