, Volume 20, Issue 1, pp 61–80 | Cite as

Continuity properties of solution maps of parametric lexicographic equilibrium problems

  • L. Q. Anh
  • T. Q. DuyEmail author
  • P. Q. Khanh


Inspired by the great importance of equilibrium problems and the lexicographic order, we consider a parametric lexicographic equilibrium problem. Sufficient conditions for the upper semicontinuity, closedness, and continuity of solution maps are established. Many examples are provided to ensure the essentialness of the imposed assumptions. Applications to lexicographic variational inequalities and lexicographic optimization problems are discussed.


Lexicographic equilibrium problems Variational inequalities and optimization Continuity Upper semicontinuity Closedness Upper and lower pseudocontinuity Relaxed monotonicity properties 

Mathematics Subject Classification

90C31 49J40 49K40 



This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.44. The authors wish to thank the anonymous referees for their helpful remarks and suggestions that helped to significantly improve the original manuscript.


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Authors and Affiliations

  1. 1.Department of Mathematics, Teacher CollegeCantho UniversityCanthoVietnam
  2. 2.Department of MathematicsUniversity of Science of Hochiminh CityHochiminh CityVietnam
  3. 3.Department of MathematicsInternational University, Vietnam National University Hochiminh CityHochiminh CityVietnam

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