On the lower semicontinuity of the solution sets for parametric generalized vector mixed quasivariational inequality problems
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1777-1795
https://doi.org/10.4134/BKMS.2015.52.6.1777
Published online November 30, 2015
Nguyen Van Hung
Dong Thap University
Abstract : 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
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