In this paper we prove the existence of solutions of regularized set-valued variational inequalities involving Br´ezis pseudomonotone operators in reflexive and locally uniformly convex Banach spaces. By taking advantage of this result, we approximate a general setvalued variational inequality with suitable regularized set-valued variational inequalities, and we show that their solutions weakly converge to a solution of the original one. Furthermore, by strengthening the coercivity conditions, we can prove the strong convergence of the approximate solutions.
- Approximate solutions
- Navies Stokes operators
- Set-valued variational inequalities