NONEMPTINESS AND BOUNDEDNESS OF SOLUTION SETS FOR PERTURBED GENERALIZED VECTOR VARIATIONAL INEQUALITIES

摘要

In this paper we study the nonemptiness and boundedness of the solution set of a perturbed generalized vector variational inequality. We obtain an existence result when the mapping involved is perturbed by a nonlinear mapping. When the mapping is perturbed along a direction, we further establish the boundedness of the solution set. We also discuss the nonemptiness and boundedness of the solution set when the constraint set is perturbed by a unit ball. Finally, we investigate the nonemptiness and boundedness of the solution set when the mapping and the constraint set are perturbed simultaneously. Our results extend the existing results for the scalar perturbed generalized variational inequality to the vector case.