Set-Valued Analysis

, Volume 16, Issue 2–3, pp 267–279 | Cite as

Semicontinuity of Solution Sets to Parametric Quasivariational Inclusions with Applications to Traffic Networks I: Upper Semicontinuities

  • Lam Quoc Anh
  • Phan Quoc Khanh


We propose some notions related to semicontinuity of a multivalued mapping and provide a clear insight for various semicontinuity-related definitions. We establish verifiable sufficient conditions for solution sets of general quasivariational inclusion problems to have these semicontinuity-related properties. Our results are proved to include and improve recent ones in the literature by corollaries and examples. Part I is devoted to upper semicontinuity properties of solution sets. Part II discusses lower semicontinuities of these sets and applications, where we discuss in details a traffic network problem as a sample for employing the main results in practical situations


Quasivariational inclusion problems Lower and upper semicontinuities Hausdorff lower and upper semicontinuities U-lower-level closedness U-upper-level closedness Quasiequilibrium problems Quasivariational inequalities Traffic network problems 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsTeacher College, Cantho UniversityCanthoVietnam
  2. 2.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam

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