Abstract
The aim of this article is to establish the existence of the solution of non-linear functional integral equations x (l, h) = U (l, h, x (l, h)) + F l, h, R l 0 R h 0 P (l, h, r, u, x (r, u)) drdu, x (l, h) G l, h, R a 0 R a 0 Q (l, h, r, u, x (r, u)) drdu, x (l, h) of two variables, which is of the form of two operators in the setting of Banach algebra C ([0, a] [0, a]), a > 0. Our methodology relies upon the measure of noncompactness related to the fixed point hypothesis. We have used the measure of noncompactness on C ([0, a] [0, a]) and a fixed point theorem, which is a generalization of Darbo's fixed point theorem for the product of operators. We additionally illustrate our outcome with the help of an interesting example.