Generalized Retarded Integral Inequalities of Gronwall Type and Applications

The integral inequalities occupy privileged position in the theory of differential and integral equations. In the recent years nonlinear integral inequalities have received considerable attention because of their important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. In 1919, Gronwall [4] introduced the famous Gronwall inequality in the study of the solutions of differential equations. There exist many lemmas which carry the name of Gronwall’s lemma. A main class may be identified is the integral inequality. The original lemma proved by Gronwall in 1919 [4], was the following