On certain power retarded Volterra-Fredholm type integralinequalities in n variables and their applications

Abstract

 This paper is devoted to investigating some new upper bounds on solutions of some nonlinear retarded integral inequalities of Volterra-Fredholm type with power in n independent variables. Our results provide a powerful generalization of some well-known Gronwall-Bellman type integral inequalities from the literature into a novel and intriguing multidimensional Volterra-Fredholm type with power. An application is given to study the boundedness of the solutions of the retarded Volterra-Fredholm type integral equation with power in n variables.