A new system of nonlinear variational-like inclusions (SNVLI) is introduced, by using the h-proximal mapping of some multi-valued operator we establish the equivalence of the problem (SNVLI) with an equality problem. Under some conditions, we also prove the convergence of the proposed Mann type iterative algorithm. We also give a simple example to show the application of our proposed algorithm.

system of variational-like inclusions, maximal h-monotone operator, h-proximal mapping, iterative algorithm, fixed point.