Journal of Optimization Theory and Applications

, Volume 133, Issue 3, pp 329–339

Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities


DOI: 10.1007/s10957-007-9190-4

Cite this article as:
Khanh, P.Q. & Luu, L.M. J Optim Theory Appl (2007) 133: 329. doi:10.1007/s10957-007-9190-4


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.


Multivalued quasivariational inequalitiesTopological vector spacesLower semicontinuityUpper semicontinuityε-Solutions

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam
  2. 2.Department of MathematicsUniversity of DalatDalatVietnam