Existence of solution for an infinite system of nonlinear integral equations via measure of noncompactness and homotopy perturbation method to solve it

摘要

In this paper we prove existence of solution for infinite system of nonlinear integral equations in the Banach spaces ℓp,p>1 with the help of a technique associated with measure of noncompactness and generalized Meir–Keeler fixed point theorem. We also provide some illustrative examples in support of our existence theorems. Finally, we introduce an iteration algorithm constructed by modified homotopy perturbation method to solve the above problem with high accuracy.