Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem

نویسندگان
Kumar, Ashish ID 1
Abbas, Syed ID 2
Rabbani, Mohsen ID 3
Deep, Amar ID 4

1 Govt. PG college Bina 470113, India

2 IIT, Mandi 175005, India

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

4 PDPM-IIITDM, Jabalpur 482005, India

doi
10.22075/ijnaa.2021.22858.2422
چکیده

In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.

کلیدواژه‌ها
Fixed point theorem, Measure of non-compactness (MNC), Banach algebra, Functional integral equation (FIE), Modified Homotopy perturbation (MHP)