We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conjecture \cite{ hayman1}, also partly answer the question given in \cite[P448]{ luolin}. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing one common value. These theorems improve the results of Luo and Lin\cite{ luolin} and some results of present authors \cite{ liuliucao}.
Categories: math.CV