# ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMS

• HUNG, NGUYEN VAN (Center of Research and Development Duy Tan University and Department of Mathematics Dong Thap University)
• 투고 : 2013.09.10
• 발행 : 2015.11.30

#### 초록

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 ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) 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.

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#### 피인용 문헌

1. Painlevé–Kuratowski convergences of the solution sets for generalized vector quasi-equilibrium problems pp.1807-0302, 2017, https://doi.org/10.1007/s40314-017-0548-4
2. Regularized gap functions and error bounds for generalized mixed strong vector quasiequilibrium problems pp.1807-0302, 2018, https://doi.org/10.1007/s40314-018-0670-y