On the existence of solutions for an infinite system of integral equations

Abstract

. The paper is devoted to prove the existence of solutions for an infinite system of non-linear integral equations. This system is investigated in the WC -Banach algebra C ( I , c 0 ) , the space of all continuous functions acting from an interval I into the sequence space c 0 . Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators acting on WC -Banach algebra involving w -contractive operators.