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We establish some new nonlinear retarded finite difference inequalities. The results that we propose here can be used as tools in the theory of certain new classes of finite difference equations in various difference situations. We also give applications of the inequalities to show the usefulness of our results [ABSTRACT FROM AUTHOR]

This paper is concerned with the boundedness and attractiveness of nonlinear switched delay systems whose subsystems have different equilibria. Some sufficient conditions which can guarantee the system's boundedness are obtained. In addition, we work out the regionwhere the solutionwill remain and furthermore the relationship between the initial function and the bounded region. Based on the new concept of attractor with switching laws, we show that the nonlinear switched delay system is attractive and then obtain the attractive region. [ABSTRACT FROM AUTHOR]