Skip to main content
SpringerLink
Log in

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lin, L. J. and Tan, N. X. On quasivariational inclusions of type I and related problems. J. Glob. Optim. 39(3), 393–407 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hai, N. X. and Khanh, P. Q. Existence of solutions to general quasiequilibrium problems and applications. J. Optim. Theory Appl. 133, 317–327 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hai, N. X. and Khanh, P. Q. The solution existence of general variational inclusion problems. J. Math. Anal. Appl. 328, 1268–1277 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hai, N. X. and Khanh, P. Q. Systems of set-valued quasivariational inclusion problems. J. Optim. Theory Appl. 135, 55–67 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lin, L. J. and Shie, H. J. Existence theorems of quasivariational inclusion problems with applications to bilevel problems and mathematical programs with equilibrium constraint. J. Optim. Theory Appl. 138, 445–457 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Lin, L. J., Wang, S. Y., and Chuang, C. S. Existence theorems of systems of variational inclusion problems with applications. J. Glob. Optim. 40, 751–764 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ding, Xieping, Lee, C. S., and Yao, J. C. Generalized constrained multiobjective games in locally FC-uniform spaces. Appl. Math. Mech. -Engl. Ed. 29(3), 301–309 (2008) DOI: 10.1007/s10483-008-0303-y

    Article  MATH  MathSciNet  Google Scholar 

  9. Ding, Xieping, Liou, Y. C., and Yao, J. C. Generalized R-KKM type theorems in topological spaces with applications. Appl. Math. Lett. 18, 1345–1350 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ding, Xieping. Generalized game and system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces. Nonlinear Anal. 68(4), 1028–1036 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Luc, D. T. Theory of vector optimization. Lectures Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Vol. 319 (1989)

    Google Scholar 

  12. Ben-El-Mechaiekh, H., Chebbi, S., Flornzano, M., and Llinares, J. V. Abstract convexity and fixed points. J. Math. Anal. Appl. 222, 138–150 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ding, Xieping. Maximal element theorems in product FC-spaces and generalized games. J. Math. Anal. Appl. 305, 29–42 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Horvath, C. D. Contractibility and generalized convexity. J. Math. Anal. Appl. 156, 341–357 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  15. Park, S. and Kim, H. Foundations of the KKM theory on generalized convex spaces. J. Math. Anal. Appl. 209, 551–571 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ding, Xieping. Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (I). Appl. Math. Mech. -Engl. Ed. 28(12), 1561–1568 (2007) DOI: 10.1007/s10483-007-1202-y

    Article  MATH  Google Scholar 

  17. Ding, Xieping. Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces. Nonlinear Anal. (2008) DOI: 10.1016/j.na.2008.01.018

  18. Kelly, J. L. General Topology, Van Nostrand, Princeton, New Jersey (1955)

    Google Scholar 

  19. Köthe, G. Topological Vector Spaces I, Springer-Verlag, Berlin, New York (1983)

    Google Scholar 

  20. Ding, Xieping. Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications (II). Appl. Math. Mech. -Engl. Ed. 28(12), 1569–1579 (2007) DOI: 10.1007/s10483-007-1203-y

    Article  MATH  Google Scholar 

  21. Tarafdar, E. Fixed point theorems in locally H-convex uniform spaces. Nonlinear Anal. 29, 971–978 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  22. Park, S. Fixed point theorems in locally G-convex spaces. Nonlinear Anal. 48, 869–879 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  23. Ding, Xieping. Generalizations of Himmelberg type fixed point theorems in locally FC-spaces. J. Sichuan Normal Univ. (NS) 29(1), 1–6 (2006)

    MATH  Google Scholar 

  24. Ding, Xieping. System of generalized vector quasi-equilibrium problems in locally FC-spaces. Acta Math. Sinica 22(5), 1529–1538 (2006)

    Article  MATH  Google Scholar 

  25. Ding, Xieping. Weak Pareto equilibria for generalized constrained multiobjective games in locally FC-spaces. Nonlinear Anal. 65, 538–545 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  26. Aubin, J. P. and Ekeland, I. Applied Nonlinear Analysis, Wiley, New York (1984)

    MATH  Google Scholar 

  27. Aliprantis, C. D. and Border, K. C. Infinite Dimensional Analysis, Springer-Verlag, New York (1994)

    MATH  Google Scholar 

  28. Fan, K. Fixed-points and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. U. S. A. 38(2), 121–126 (1952)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P. R. China

    Xie-ping Ding  (丁协乎)

Authors
  1. Xie-ping Ding  (丁协乎)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xie-ping Ding  (丁协乎).

Additional information

(Contributed by Xie-ping DING)

Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 07ZA092) and the Sichuan Province Leading Academic Discipline Project (No. SZD0406)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, Xp. Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces. Appl. Math. Mech.-Engl. Ed. 30, 263–274 (2009). https://doi.org/10.1007/s10483-009-0301-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-009-0301-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation