On solutions vanishing at infinity of infinite systems of quadratic Urysohn integral equations

The paper is devoted to present a result on the existence of solutions of an infinite system of quadratic integral equations of the Urysohn type considered on the real half-axis. Our investigations are conducted in the Banach space consisting of bounded and continuous functions defined on the real half-axis with values in the space of real sequences converging to zero. That space is equipped with the standard supremum norm. The main tools used in our study is the technique of measures of noncompactness and the Schauder fixed point principle. We illustrate our result by a suitable example.