Bulletin of the
Korean Mathematical Society BKMS

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function $u$ in the right-hand side of the inequality (1.2) is replaced by the function $u^p$ for some $p. $ These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

Keywords: Gronwall-type inequalities, integral equation, integral inequality, iterated integrals

MSC numbers: 26D15, 35A05