Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1<p<\infty)$ and $c_{0}$

Abstract

In this paper, by applying the technique of measure of noncompactness and a new generalization of Darbo’s theorem, we study the existence of solutions for an infinite system of integral equations in two variables. The obtained results extend and generalize some related results in previous work. Finally, some examples are included to ascertain the usefulness of the outcome.

Keywords

• banach spaces $\ell_{p}$ and $c_{0}$
• darbo's fixed point theorem
• measure of noncompactness
• integral equations