On a functional Volterra-Fredholm integral equation, via Picard operators

Abstract

Abstract. In this paper we present some results relative to existence, uniqueness, integral in-equalities and data dependence for the solutions of the functional Volterra-Fredholm integral equation with deviating argument in a Banach space: u(x,y) = g(x,y,h(u)(x,y))+ ∫ x 0 ∫ y 0 K(x,y,s,t,u(s,t))dsdt, x,y ∈ R+ by Picard operators technique. This equation is a generalization of the equation (VF) from the paper: B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstratio Math., 40(2007), No. 4, 832-852. 1.