Bulletin of the
Korean Mathematical Society BKMS

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition {\rm($H_h(\gamma_0, \lambda_0, \mu_0)$)} is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

Keywords: parametric generalized vector mixed quasivariational inequality problem, parametric gap function, inner-openness, lower semicontinuity, Hausdorff lower semicontinuity, continuity, H-continuity

MSC numbers: 90C31, 49J53, 49J40, 49J45