10.1007/s40096-016-0176-y

Lower semicontinuity of solutions for order-perturbed parametric vector equilibrium problems

XML HTML PDF
  • Shunyou Xia*1,
  • Shuwen Xiang2,
  • Yanlong Yang2,
  • Deping Xu3,
  1. School of Mathematics and Computer Science, Guizhou Education University, Guiyang, 550018, CN College of Computer Science and Technology, Guizhou University, Guiyang, 550025, CN
  2. College of Computer Science and Technology, Guizhou University, Guiyang, 550025, CN
  3. College of Information Management, Chengdu University of Technology, Chengdu, 610059, CN

Published in Issue 2016-04-22

How to Cite

Xia, S., Xiang, S., Yang, Y., & Xu, D. (2016). Lower semicontinuity of solutions for order-perturbed parametric vector equilibrium problems. Mathematical Sciences, 10(1-2 (June 2016). https://doi.org/10.1007/s40096-016-0176-y
Crossref
Scopus
Google Scholar
Europe PMC

HTML views: 15

PDF views: 108

Abstract

Abstract The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established. Some examples are developed to illustrate our results are real generalization different from recent ones in the literature and to describe the essential conditions of the latest results in the references are not real essential.

Keywords

  • Order-perturbed parametric vector equilibrium problems,
  • Lower semicontinuity,
  • Cone lower semicontinuity,
  • Efficient solutions
HTML PDF

References

  1. Anh and Khanh (2004) Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems (pp. 699-711) https://doi.org/10.1016/j.jmaa.2004.03.014
  2. Anh and Khanh (2008) Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks II. Lower semicontinuities applications (pp. 943-960) https://doi.org/10.1007/s11228-008-0082-z
  3. Anh and Khanh (2010) Continuity of solution maps of parametric quasiequilibrium problems (pp. 247-259) https://doi.org/10.1007/s10898-009-9422-2
  4. Gong and Yao (2008) Lower semicontinuity of the set of efficient solutions for generalized systems (pp. 197-205) https://doi.org/10.1007/s10957-008-9379-1
  5. Gong (2008) Continuity of the solution set to parametric weak vector equilibrium problems (pp. 35-46) https://doi.org/10.1007/s10957-008-9429-8
  6. Han and Gong (2014) Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems (pp. 38-41) https://doi.org/10.1016/j.aml.2013.09.006
  7. Huang et al. (2006) Stability for parametric implicit vector equilibrium problems (pp. 1267-1274) https://doi.org/10.1016/j.mcm.2005.06.010
  8. Chen and Huang (2012) Continuity of the solution mapping to parametric generalized vector equilibrium problems (pp. 1515-1528) https://doi.org/10.1007/s10898-012-9904-5
  9. Chen et al. (2009) Solution semicontinuity of parametric generalized vector equilibrium problems (pp. 309-318) https://doi.org/10.1007/s10898-008-9376-9
  10. Li and Fang (2010) Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality (pp. 507-515) https://doi.org/10.1007/s10957-010-9736-8
  11. Li et al. (2013) Continuity of the solution mappings to parametric generalized strong vector equilibrium problems (pp. 597-610) https://doi.org/10.1007/s10898-012-9985-1
  12. Li and Li (2014) Hölder continuity of perturbed solution set for convex optimization problems (pp. 908-918)
  13. Kimura and Yao (2008) Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems (pp. 187-202) https://doi.org/10.1007/s10898-007-9210-9
  14. Cheng and Zhu (2005) Global stability results for the weak vector variational inequality (pp. 543-550) https://doi.org/10.1007/s10898-004-2692-9
  15. Zhang et al. (2013) A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems (pp. 469-472) https://doi.org/10.1016/j.aml.2012.11.010
  16. Wangkeeree et al. (2014) Continuity of the solution mappings to parametric generalized vector equilibrium problems (pp. 42-45) https://doi.org/10.1016/j.aml.2013.10.012
  17. Kien (2005) On the lower semicontinuity of optimal solution sets (pp. 123-130) https://doi.org/10.1080/02331930412331330379
  18. Aubin and Ekeland (1984) Wiley
  19. Ferro (1989) A minimax theorem for vector-valued functions (pp. 19-31) https://doi.org/10.1007/BF00938796