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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Hochiminh City, Vietnam

    P. Q. Khanh

  2. Department of Mathematics, University of Dalat, Dalat, Vietnam

    L. M. Luu

Authors
  1. P. Q. Khanh
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  2. L. M. Luu
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Corresponding author

Correspondence to P. Q. Khanh.

Additional information

Communicated by S. Schaible.

This research was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The final part of this work was completed during a stay of the first author at the Department of Mathematics, University of Pau, Pau, France, and its hospitality is acknowledged.

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Khanh, P.Q., Luu, L.M. Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities. J Optim Theory Appl 133, 329–339 (2007). https://doi.org/10.1007/s10957-007-9190-4

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  • DOI: https://doi.org/10.1007/s10957-007-9190-4

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