On some generalizations of certain nonlinear retarded integral inequalities for Volterra-Fredholm integral equations and their applications in delay differential equations

By some new analysis techniques, we generalize the results presented by Pachpatte in [Integral and Finite Difference Inequalities and Applications, volume 205, Elsevier, 2006] and and by S. D. Kendre in [Some nonlinear integral inequalities for Volterra-Fredholm integral equations, Adv. Inequal. App, 2014:Article 21, 2014.] to nonlinear retarded inequalities, and investigate also some new forms. Some applications are also presented in order to illustrate the usefulness of some of our results.