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ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMS
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 Title & Authors
ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMS
HUNG, NGUYEN VAN;
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 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
1.
Painlevé–Kuratowski convergences of the solution sets for generalized vector quasi-equilibrium problems, Computational and Applied Mathematics, 2017, 1807-0302  crossref(new windwow)
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