Existence of Solutions for an Infinite System of Quadratic Integral Equations in the Banach Algebra C(I,c(0))

摘要

The paper is devoted to prove the existence of solutions for an infinite system of nonlinear quadratic integral equations. This system is investigated in the WC-Banach algebra C0 = C(I, c0), consisting of all continuous functions acting from an interval I into the sequence space c0. The assumptions imposed on the operators involving the system are formulated in terms of a generalized Lipschitz continuity.