Skip to main content
Log in

Mixed generalized quasi-equilibrium problems

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

Abstract

In this paper, we introduce mixed generalized quasi-equilibrium problems and show some sufficient conditions on the existence of their solutions. As special cases, we obtain several results for different mixed quasi-equilibrium problems, mixed quasi-variational inclusions problems and mixed quasi-relation problems etc.

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

Access this article

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. Balaj M., Luc D.T.: On mixed variational relation problems. Comput. Math. Appl. 60(9), 2712–2722 (2010)

    Article  Google Scholar 

  2. Duong T.T.T., Tan N.X.: On the existence of solutions to generalized quasi-equilibrium problems of type I and related problems. Adv Nonlinear Var Inequal. 13(1), 29–47 (2010)

    Google Scholar 

  3. Duong T.T.T., Tan N.X.: On the existence of solutions to generalized quasi-equilibrium problems. J. Global Optim. 52(4), 711–728 (2011)

    Article  Google Scholar 

  4. Ferro F.: A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 60, 19–31 (1989)

    Article  Google Scholar 

  5. Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems and Variational Models. Kluwer, Dordrecht (2001)

    Google Scholar 

  6. Kim W.K., Tan K.K.: New existence theorems of equilibria and applications. Nonlinear Anal. 47, 531–542 (2001)

    Article  Google Scholar 

  7. Li X.B., Li S.J.: Existence of solutions for generalized vector quasi-equilibrium problems. Optim. Lett. 4(1), 17–28 (2010)

    Article  Google Scholar 

  8. Lin L.J.: Systems of generalized quasivariational inclusion problems with applications to variational analysis and optimization problems. J. Global Optim. 38, 21–39 (2007)

    Article  Google Scholar 

  9. Lin L.J., Tu C.I.: The studies of systems of variational inclusions problems and variational disclusions problems with applications. Nonlinear Anal. TMA 69, 1981–1998 (2008)

    Article  Google Scholar 

  10. Lin L.J., Tan N.X.: On quasivariational inclusion problems of type I and related problems. J. Global Optim. 39(3), 393–407 (2007)

    Article  Google Scholar 

  11. Lin L.J., Tan N.X.: Quasi-equilibrium inclusion problems of Blum-Oetli type and related problems. Acta Math. Vietnam 34(1), 111–123 (2009)

    Google Scholar 

  12. Lin L.J., Wang S.Y: Simultaneuous variational relations problem and related application. Comput. Math. Appl. 58, 1711–1721 (2009)

    Article  Google Scholar 

  13. Luc D.T.: An abstract problem in variational analysis. J. Optim. Theory Appl. 138, 65–76 (2008)

    Article  Google Scholar 

  14. Luc D.T., Tan N.X.: Existence conditions in variational inclusions with constraints. Optimization 53, 505–515 (2004)

    Article  Google Scholar 

  15. Minh N.B., Tan N.X.: Some sufficient conditions for the existence of equilibrium points concerning multivalued mappings. Vietnam J. Math. 28, 295–310 (2000)

    Google Scholar 

  16. Minh N.B., Tan N.X.: On the existence of solutions of quasivariational inclusion problems of Stampacchia type. Adv. Nonlinear Var. Inequal. 8, 1–16 (2005)

    Google Scholar 

  17. Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)

    Book  Google Scholar 

  18. Peng J.-W., Wu S.-Y.: The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems. Optim. Lett. 4(4), 501–512 (2010)

    Article  Google Scholar 

  19. Sach P.H., Tuan L.A.: Existence results for set-valued vector quasiequilibrium problems. J. Optim. Theory Appl. 133, 229–240 (2007)

    Article  Google Scholar 

  20. Tan N.X.: On the existence of solutions of quasi-variational inclusion problems. J. Optim. Theory Appl. 123, 619–638 (2004)

    Article  Google Scholar 

  21. Tuan L.A., Sach P.H.: Existence of solutions of generalized quasivariational inequalities with set-valued maps. Acta Math. Vietnam 29, 309–316 (2004)

    Google Scholar 

  22. Tuan L.A., Sach P.H.: Generalizations of vector quasivariational inclusion problems with set-valued maps. J. Global Optim. 43(1), 23–45 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Truong Thi Thuy Duong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Duong, T.T.T. Mixed generalized quasi-equilibrium problems. J Glob Optim 56, 647–667 (2013). https://doi.org/10.1007/s10898-012-9891-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-012-9891-6

Keywords

Mathematics Subject Classification

Navigation