Generalizations of R0 and SSM properties; Extended Horizontal Linear Complementarity Problem

In this paper, we first introduce R0-W and SSM-W properties for the set of matrices which is a generalization of R0 and the strictly semimonotone matrix. We then prove some existence results for the extended horizontal linear complementarity problem when the involved matrices have these properties. With an additional condition on the set of matrices, we prove that the SSM-W property is equivalent to the unique solution for the corresponding extended horizontal linear complementarity problems. Finally, we give a necessary and sufficient condition for the connectedness of the solution set of the extended horizontal linear complementarity problems.