On some new integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions and their applications

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions are established. These inequalities generalize and improve some former famous results about inequalities, and which provide an excellent tool to discuss the qualitative and quantitative properties for solutions to some nonlinear differential and integral equations. To illustrate our results, we present an example to show estimated solutions for an impulsive differential system.