Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness

The aim of this paper is to establish fixed point theorems for condensing operators in the Fréchet spaces. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tychonoff fixed point theorem. Moreover, as an application, we study the problem of the existence of solutions for infinite systems of integral equations in two variables. The results obtained extend several ones. Finally, an example is presented to show the efficiency of our results.