Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients

In this paper, we consider the nonexistence of eventually positive solutions of the difference inequality Let m be a positive integer. Then for each positive integer i: 1 ≤ i ≤ m, {ki(n)}∞n=0 and {pi(n)}∞n=0 are a sequence of positive integers and a sequence of nonnegative real numbers, respectively. A sufficient condition guaranteeing the nonexistence of eventually positive solutions is obtained with the help of a new method. As an application of the main result, a conjecture is proved.