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.

在一些弱条件下，在Banach代数空间\（C（[0，b] \ times [0，b]，\ mathbb {R}），b>中，建立了两个变量泛函积分方程解的存在性0 \），形式为两个运算符。我们为上述空间中的算子应用了非紧致性度量（简称MNC）和Petryshyn不动点定理的概念。为了应用我们定理的结果，给出了一个有趣的例子。为了计算该示例的解，我们使用了一种迭代算法，该算法是通过修改的同伦摄动方法和Adomian多项式构造的，具有可接受的精度。