In this article, solvability of infinite system of nonlinear singular integral equations of two variables in Banach sequence spaces \(c_{0}\) and \(\ell _{1}\) is investigated. For this purpose, Hausdorff measure of noncompactness (in short, Hausdorff MNC) and Meir–Keeler condensing operators are employed. The guarantee of our results are given by some examples. Also to approach an approximation of semi-analytic solution, we introduce a coupled modified homotopy perturbation and Adomian decomposition method. Thus, an iterative algorithm is constructed to find the above solution. The numerical results show that the produced sequence to approximate the solution has a high accuracy.

本文研究了Banach序列空间\（c_ {0} \）和\（\ ell _ {1} \）中两个变量的非线性奇异积分方程的无限系统的可解性。为此，采用了非紧密度的Hausdorff量度（简称Hausdorff MNC）和Meir-Keeler冷凝算子。通过一些例子可以保证我们的结果。另外，为了逼近半解析解，我们引入了一种修正的同伦摄动和Adomian分解耦合方法。因此，构造了迭代算法以找到上述解决方案。数值结果表明，所产生的近似解序列具有较高的精度。