Document Type : Research Paper

Authors

• Anupam Das ¹
• Mohsen Rabbani ²
• Bipan Hazarika ^{1, 3}
• Reza Arab ²

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.

Keywords

• Measure of noncompactness
• Infinite systems of singular integral equations
• Meir-Keeler condensing operators
• Fixed point theorem
• Modified homotopy perturbation‎