Existence of solutions of infinite systems of integral equations in the Frechet spaces

In this paper we apply the technique of measures of noncompactness to the theory of innite system of integral equations in the Frechet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for innite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychonoff fixed point theorem. Also, we present an example of nonlinear integral equations to show the effciency of our results. Our results extend several comparable results obtained in the previous literature.