Some point-wise estimates for solutions of a class of nonlinear functional-integral inequalities

Summary The celebrated Gronwall-Bellman Lemma provides explicit bounds on solutions of a class of linear integral inequalities. The aim of this paper is to prove sufficiently general results analogous to this Lemma for functional-integral inequalities. These results are useful for obtaining point-wise estimates or comparison theorems for solutions of functional differential equations and functional-integral equations of Volterra type. Entrata in Redazione il 1^o settembre 1971.