On the existence of solution to a class of nonlinear functional integral equations with two variables

Document Type : Research Paper

Authors

1 Mathematics Discipline, IIITDM, Jabalpur 482005 (MP), India

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

3 Department of Mathematics, Izmir Institute of Technology, Izmir, Turkiye

10.22075/ijnaa.2024.34255.5112

Abstract

In this article, the existence of a solution for non-linear functional integral equations with two variables is considered in Banach space C([0,b]×[0,c]) by applying Petryshyn's fixed point theorem. Our focus extends to diverse instances of functional integral equations encountered within mathematical analysis. Our study's effectiveness is demonstrated through an example. Furthermore, to confirm the reliability of our proposed approach, we introduce an iterative algorithm via Sinc interpolation, which effectively achieves a precise, approximate solution.

Keywords

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Articles in Press, Corrected Proof
Available Online from 03 February 2025
  • Receive Date: 27 May 2024
  • Revise Date: 08 August 2024
  • Accept Date: 08 August 2024