On some new nonlinear retarded integral inequalities with iterated integrals and their applications

Some new nonlinear retarded integral inequalities of Gronwall- like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.