### Solvability of infinite system of nonlinear singular integral equations in the $C(I\times‎ I‎, ‎c)$ space and modified semi-analytic method to find a closed-form of solution

Document Type : Research Paper

Authors

1 Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India

2 Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

3 Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India

Abstract

‎In this article‎, ‎we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I \times I‎, ‎c)$ by applying measure of noncompactness‎ and Meir-Keeler condensing operators‎. By presenting an example, we have illustrated our results‎. ‎For validity of the results we introduce a modified semi-analytic method in the case of two variables to make an iteration algorithm to find a closed-form of solution for the above problem‎. ‎The numerical results show that the produced sequence for approximating the solution of example is in the $c$ space with a high accuracy‎.

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