Strongly convergent inertial projection and contraction methods for split variational inequality problem

In the literature, several methods have been proposed for solving the split variational inequality problems and most of these methods require that the underlying operators are co-coercive while some of them require that the problem is transformed into a product space. These restrictive conditions affect the feasibility of these existing methods. In order to overcome these setbacks, we propose two new inertial projection and contraction methods for solving the split variational inequality problem in real Hilbert spaces without the co-coercive condition and without the product space formulation, which does not fully exploit the attractive splitting structure of the split variational inequality problem. The sequences generated by these methods converge strongly to the solution of the split varitional inequality problems in real Hilbert spaces under the assumptions that the operators are pseudomonotone, Lipschitz continuous and without the sequentially weakly continuity condition. Furthermore, we present several numerical experiments for the proposed methods and compare their performance with other related methods in the literature.