Skip to main content
SpringerLink
Log in

Existence Results for Systems of Vector Equilibrium Problems*

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

The purpose of this paper is to study systems of vector equilibrium problems. We establish some existence theorems for systems of vector equilibrium problems by using (S)+-conditions and Kakutani–Fan–Glicksberg fixed point theorem

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Q.H. Ansari J.C. Yao (1999) ArticleTitleA fixed point theorem and its applications to a system of variational inequalities Bulletin of the Australian Mathematical Society 59 IssueID3 433–442 Occurrence Handle10.1017/S0004972700033116

    Article  Google Scholar 

  2. Q.H. Ansari J.C. Yao (2000) ArticleTitleSystems of generalized variational inequalities and their applications Applicable Analysis 76 IssueID3–4 203–217

    Google Scholar 

  3. Q.H. Ansari S. Schaible J.C. Yao (2000) ArticleTitleSystem of vector equilibrium problems and its applications Journal of Optimization Theory and Applications 107 IssueID3 547–557 Occurrence Handle10.1023/A:1026495115191

    Article  Google Scholar 

  4. Q.H. Ansari S. Schaible J.C. Yao (2002) ArticleTitleThe system of generalized vector equilibrium problems with applications. Journal of Global Optimizations 22 3–16 Occurrence Handle10.1023/A:1013857924393

    Article  Google Scholar 

  5. Q.H. Ansari W.K. Chan X.Q. Yang (2004) ArticleTitleThe system of vector quasi- equilibrium problems with applications Journal of Global Optimization 29 IssueID1 45–57 Occurrence Handle10.1023/B:JOGO.0000035018.46514.ca

    Article  Google Scholar 

  6. P. Deguire K.K. Tan G.X.Z. Yuan (1999) ArticleTitleThe study of maximal elements, fixed points for Ls-majorized mappings and their applications to minimax and variational inequalities in product topological spaces Nonlinear Analysis 37 IssueID7 933–951 Occurrence Handle10.1016/S0362-546X(98)00084-4

    Article  Google Scholar 

  7. G. Kassay J. Kolumbán (2000) ArticleTitleSystem of multi-valued variational inequalities Publications Mathematicae Debrecen 56 185–195

    Google Scholar 

  8. G. Kassay J. Kolumbán Z. Páles (2002) ArticleTitleFactorization of Minty and Stampacchia variational inequality system European Journal of Operational Research 143 IssueID2 377–389 Occurrence Handle10.1016/S0377-2217(02)00290-4

    Article  Google Scholar 

  9. Y.P. Fang N.J. Huang (2004) ArticleTitleExistence results for systems of strong implicit vector variational inequalities Acta Mathematica Hungarica 103 IssueID4 265–277 Occurrence Handle10.1023/B:AMHU.0000028828.52601.9e

    Article  Google Scholar 

  10. Y.P. Fang N.J. Huang J.K. Kim (2003) ArticleTitleA system of multi-valued generalized order complementary problems in ordered metric spaces Zeitschrift für Analysis und ihre Anwendungen 22 IssueID4 779–788

    Google Scholar 

  11. J.Y. Fu (2003) ArticleTitleSymmetric vector quasi-equilibrium problems Journal of Mathematical Analysis and Applications 285 IssueID2 708–713 Occurrence Handle10.1016/S0022-247X(03)00479-7

    Article  Google Scholar 

  12. N.J. Huang Y.P. Fang (2003) ArticleTitleFixed point theorems and a new system of multivalued generalized order complementarity problems Positivity 7 257–265 Occurrence Handle10.1023/A:1026222030596

    Article  Google Scholar 

  13. G. Kassay J. Kolumbán Z. Páles (1999) ArticleTitleOn Nash stationary points Publicationes Mathematicae Debrecen 54 267–279

    Google Scholar 

  14. Y.S. Lai Y.G. Zhu Y.B. Deng (2003) ArticleTitleThe existence of nonzero solutions for a class of variational inequalities by index Applied Mathematics Letters 16 IssueID6 839–845 Occurrence Handle10.1016/S0893-9659(03)90005-X

    Article  Google Scholar 

  15. R.U. Verma (2001) ArticleTitleProjection methods, algorithms, and a new system of nonlinear variational inequalities Computers & Mathematics with Applications 41 IssueID7–8 1025–1031 Occurrence Handle10.1016/S0898-1221(00)00336-9

    Article  Google Scholar 

  16. R.U. Verma (2004) ArticleTitleGeneralized system for relaxed cocoercive variational inequalities and projection methods Journal of Optimization Theory and Applications 121 IssueID1 203–210 Occurrence Handle10.1023/B:JOTA.0000026271.19947.05

    Article  Google Scholar 

  17. Y.G. Zhu (1998) ArticleTitlePositive solution to a system of variational inequalities Applied Mathematics Letters 11 IssueID4 63–70 Occurrence Handle10.1016/S0893-9659(98)00057-3

    Article  Google Scholar 

  18. T. Tanaka (1997) ArticleTitleGeneralized semicontinuity and existence theorems for cone saddle points Applied Mathematics and Optimization 36 313–322 Occurrence Handle10.1007/s002459900065

    Article  Google Scholar 

  19. Y. Chiang O. Chadli J.C. Yao (2003) ArticleTitleExistence of solutions to implicit vector variational inequalities Journal of Optimization Theory and Applications 116 IssueID2 251–264 Occurrence Handle10.1023/A:1022472103162

    Article  Google Scholar 

  20. Q.H. Ansari X.Q. Yang J.C. Yao (2001) ArticleTitleExistence and duality of implicit vector variational problems Numerical Functional Analysis & Optimizations 22 IssueID7–8 815–829 Occurrence Handle10.1081/NFA-100108310

    Article  Google Scholar 

  21. O. Chadli Y. Chiang S. Huang (2002) ArticleTitleTopological pseudomonotonicity and vector equilibrium problems Journal of Mathematical Analysis and Applications 270 435–450 Occurrence Handle10.1016/S0022-247X(02)00079-3

    Article  Google Scholar 

  22. Y. Chiang J.C. Yao (2004) ArticleTitleVector variational inequalities and (S)+-conditions Journal of Optimization Theory and Applications 123 IssueID2 271–290 Occurrence Handle10.1007/s10957-004-5149-x

    Article  Google Scholar 

  23. J.S. Guo J.C. Yao (1994) ArticleTitleVariational inequalities with nonmonotone operators Journal of Optimization Theory and Applications 80 63–74 Occurrence Handle10.1007/BF02196593

    Article  Google Scholar 

  24. O. Chadli N.C. Wong J.C. Yao (2003) ArticleTitleEquilibrium problems with applications to eigenvalue problems Journal of Optimization Theory and Applications 117 IssueID2 245–266 Occurrence Handle10.1023/A:1023627606067

    Article  Google Scholar 

  25. Y.P. Fang N.J. Huang (2004) ArticleTitleVector equilibrium type problems with (S)+- condition Optimization 53 IssueID3 269–279 Occurrence Handle10.1080/02331930410001712652

    Article  Google Scholar 

  26. M. Bianchi S. Schaible (1996) ArticleTitleGeneralized monotone bifunctions and equilibrium problems Journal of Optimization Theory and Applications 90 31–43 Occurrence Handle10.1007/BF02192244

    Article  Google Scholar 

  27. X.P. Ding (2000) ArticleTitleExistence of solutions for quasi-equilibrium problems in noncompact topological spaces Computers & Mathematics with Applications 39 IssueID3–4 13–21 Occurrence Handle10.1016/S0898-1221(99)00329-6

    Article  Google Scholar 

  28. Y.P. Fang N.J. Huang (2003) ArticleTitleThe vector F-complementary problems with demipseudomonotone mappings in Banach spaces Applied Mathematics Letters 16 1019–1024 Occurrence Handle10.1016/S0893-9659(03)90089-9

    Article  Google Scholar 

  29. F. Giannessi (Eds) (2000) Vector Variational Inequalities and Vector Equilibria Kluwer Academic Publishers Dordiechet, Holland

    Google Scholar 

  30. N. Hadjisavvas S. Schaible (1998) ArticleTitleFrom scalar to vector equilibrium problems in the quasimonotone case Journal of Optimization Theory and Applications 96 297–309 Occurrence Handle10.1023/A:1022666014055

    Article  Google Scholar 

  31. I.V. Konnov S. Schaible (2000) ArticleTitleDuality for equilibrium problems under generalized monotonicity Journal of Optimization Theory and Applications 104 395–408 Occurrence Handle10.1023/A:1004665830923

    Article  Google Scholar 

  32. L.J. Lin Z.T. Yu G. Kassay (2002) ArticleTitleExistence of equilibria for multivalued mappings and its application to vectorial equilibria Journal of Optimization Theory and Applications 114 189–208 Occurrence Handle10.1023/A:1015420322818

    Article  Google Scholar 

  33. F.E. Browder (1970) ArticleTitlePseudo-monotone operators and direct method of the calculus of variations Archive for Rational Mechanic and Analysis 38 268–277 Occurrence Handle10.1007/BF00281524

    Article  Google Scholar 

  34. F.E. Browder (1983) ArticleTitleFixed-point theory and nonlinear problems Bulletin of the American Mathematical Society 9 1–39 Occurrence Handle10.1090/S0273-0979-1983-15153-4

    Article  Google Scholar 

  35. I. Glicksberg (1952) ArticleTitleA further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points Proceedings of the American Mathematical Society 3 170–174 Occurrence Handle10.2307/2032478

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China

    Ya-Ping Fang & Nan-Jing Huang

  2. Department of Mathematics, Kyungnam University, Masan, Kyungnam, 631-701, Korea

    Jong Kyu Kim

Authors
  1. Ya-Ping Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nan-Jing Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jong Kyu Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya-Ping Fang.

Additional information

*This work was supported by the Kyungnam University Research Fund 2004

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fang, YP., Huang, NJ. & Kim, J.K. Existence Results for Systems of Vector Equilibrium Problems*. J Glob Optim 35, 71–83 (2006). https://doi.org/10.1007/s10898-005-1654-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-005-1654-1

Keywords

Mathematics Subject Classification (2000)

Search

Navigation