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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 6, 2015, pp.1777-1795
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.6.1777

Title & Authors

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

HUNG, NGUYEN VAN;

HUNG, NGUYEN VAN;

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 ((, , )) 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;

Language

English

Cited by

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