The aim of this paper is to study the existence of asymptotically stable solutions for a mixed functional integral equation in N variables. This is done by using a fixed point theorem of Krasnosel’skii type in the Frechet space and the new integral inequalities with explicit estimate. In order to illustrate the results obtained here, an example is given. Mathematics subject classification (2010): 47H10, 45G10, 47N20, 65J15.