Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness

In this paper, we analyze the existence of solution for two-dimensional nonlinear Volterra integral equations (2DVIE) by using the techniques of measures of noncompactness and Petryshyn fixed point theorem which contains as particular cases a lot of integral and functional-integral equations that arise in nonlinear analysis. Also some illustrative examples are given.