Asymptotic Behavior of Some Differential Inequalities with Mixed Delays and Their Applications

In this paper, we focus on the asymptotic stability of the trajectories governed by the differential inequalities with mixed delays using the fixed-point theorem. It is interesting that the Halanay inequality is a special case of the differential inequality studied in this paper. Our results generalize and improve the existing results on Halanay inequality. Finally, three numerical examples are utilized to illustrate the effectiveness of the obtained results.