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Zbl 1146.49006
Khanh, P.Q.; Luu, L.M.
Lower semicontinuity and upper semicontinuity of the solution sets and approximate solution sets of parametric multivalued quasivariational inequalities. (English)
[J] J. Optim. Theory Appl. 133, No. 3, 329-339 (2007). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We consider the semicontinuity of the solution set and the approximate solution set of parametric multivalued quasivariational inequalities in topological vector spaces. Three kinds of problems arising from the multivalued situation are investigated. A rather complete picture, which is symmetric for the two kinds of semicontinuity (lower and upper semicontinuity) and for the three kinds of multivalued quasivariational inequality problems, is supplied. Moreover, we use a simple technique to prove the results. The results obtained improve several known ones in the literature.

MSC 2000:: *49J40 Variational methods including variational inequalities
49J53 Set-valued and variational analysis
47J20 Inequalities involving nonlinear operators

Keywords: multivalued quasivariational inequalities; topological vector spaces; lower semicontinuity; upper semicontinuity; $\epsilon$-solutions

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