On the existence of solutions for the variational inequality problem V I(A, \psi, \phi,g;K)

In this paper, we are concerned with the existence of a solution u ۲ K for the variational inequality problem V I(A; \psi, \phi, g;K). Furthermore, we propose some conditions that ensure the well-posedness of this problem. We study an operator type g - ql which extends the linear problem. Finally, we investigate the existence of solutions for general vector variational inequalities in the inclusion form.

Keywords:

variational inequality , Type g-ql , GKKM mapping , well-posedness , Approximating sequence and Value cone set