Existence of solution of infinite systems of singular integral equations of two variables in $C(I \times I,\ell_{p})$ with $I=[0,T],T>0$ and $1

Abstract

In this article,  we discuss  the  solvability of  infinite systems of singular integral equations of two variables in the Banach sequence spaces  $C(I \times I,\ell_{p})$ with $I=[0,T],T>0$ and $1<p<\infty$ by applying Hausdorff measure of noncompactness with the help of Meir-Keeler condensing operators. We illustrate our results with the help of an example.