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

In this article, the existence of a solution for non-linear functional integral equations with two variables is considered in Banach space C([۰, b]\times [۰, 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.

کلیدواژه ها:

Fixed point theorem (FPT) ، Measure of non-compactness(MNC) ، Functional integral equation