On some generalized non-linear functional integral equations of two variables via measures of noncompactness and numerical method to solve it

Abstract

Existence of solution for functional integral equations of two variables is established in this article under some weaker conditions in a Banach algebra space $$C([0, b]\times [0, b],\mathbb {R}), b>0$$ in the form of two operators. We applied the concept of measure of non-compactness (in short, MNC) and Petryshyn fixed point theorem for the operators in the above-mentioned space. For applicability of the obtained results of our theorem, an interesting example is given. To compute the solution of the example, we used an iterative algorithm which was constructed by modified homotopy perturbation method and Adomian polynomials with an acceptable accuracy.