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Das, Anupam, Rabbani, Mohsen, Hazarika, Bipan, Arab, Reza. (1398). 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. نشریه هنرهای کاربردی, 10(1), 63-76. doi: 10.22075/ijnaa.2019.16525.1875
Anupam Das; Mohsen Rabbani; Bipan Hazarika; Reza Arab. "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". نشریه هنرهای کاربردی, 10, 1, 1398, 63-76. doi: 10.22075/ijnaa.2019.16525.1875
Das, Anupam, Rabbani, Mohsen, Hazarika, Bipan, Arab, Reza. (1398). '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', نشریه هنرهای کاربردی, 10(1), pp. 63-76. doi: 10.22075/ijnaa.2019.16525.1875
Das, Anupam, Rabbani, Mohsen, Hazarika, Bipan, Arab, Reza. 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. نشریه هنرهای کاربردی, 1398; 10(1): 63-76. doi: 10.22075/ijnaa.2019.16525.1875

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

International Journal of Nonlinear Analysis and Applications
مقاله 7، دوره 10، شماره 1، بهمن 2019، صفحه 63-76    اصل مقاله (149.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.16525.1875
نویسندگان
Anupam Das1؛ Mohsen Rabbani* 2؛ Bipan Hazarika1، 3؛ Reza Arab2
1Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India
2Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
3Department of Mathematics, Gauhati University, Guwahati-781014, Assam, India
تاریخ دریافت: 27 آبان 1397،  تاریخ بازنگری: 28 دی 1397،  تاریخ پذیرش: 04 بهمن 1397 
چکیده
‎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.
کلیدواژه‌ها
Measure of noncompactness؛ Infinite systems of singular integral equations؛ Meir-Keeler condensing operators؛ Fixed point theorem؛ Modified homotopy perturbation‎
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