Solvability of Infinite Systems of Nonlinear Integral Equations in Two Variables by Using Semi-Analytic Method

Abstract

‎In this article‎, ‎we generalize and investigate existence of solution for infinite systems of nonlinear integral equations with two variables in a given Banach sequence space $BC(\mathbb{R}_{+} \times \mathbb{R}_{+},c )$‎

‎using Meir-Keeler condensing and noncompactness operators‎. ‎Validity of results are shown with the help of an illustrative example‎. ‎We also introduce a coupled semi-analytic method in the case of two variables in order to construct an iteration algorithm to find a numerical solution for above-mentioned problem‎. ‎The numerical results show that the produced sequence for approximating the solution in the examples is in the Banach sequence space $BC(\mathbb{R}_{+} \times \mathbb{R}_{+},c )$ itself‎.