New oscillation criteria for first-order delay difference equations

In this paper, some new oscillation criteria are obtained for the first-order delay difference equation x n + 1 − x n + k k ( k + 1 ) k + 1 x n - k + f ( n , x n − l 1 , … , x n − l s ) = 0 , n = 0 , 1 , 2 , … , , where k,l 1,l 2,, l s are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results.