generalization of darbo’s fixed point theorem via the measure of noncompactness for solving a system of implicit integral equations

In this paper, we study the existence of solutions to a system of implicit integral functional equations involving a nonlinear operator in the space ????????(ℝ+ 3 ). by employing the concept of the measure of noncompactness together with a generalized version of darbo’s fixed point theorem adapted to the three-dimensional case, we establish sufficient conditions for boundedness, continuity, and weak contraction of the associated operators. using these results, we prove that the considered system admits at least one solution in the space ????????(ℝ+ 3 ).