Skip to main content
SpringerLink
Log in

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

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

Abstract

By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclusion) problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

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. Robinson, S. M. Generalized equation and their solutions, part I: basic theory. Math. Program. Study 10(1), 128–141 (1979)

    MATH  Google Scholar 

  2. Hassouni, A. and Moudafi, A. A perturbed algorithm for variational inclusions. J. Math. Anal. Appl. 185(3), 706–721 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Adly, S. Perturbed algorithms and sensitivity analysis for a general class of variational inclusions. J. Math. Anal. Appl. 201(3), 609–630 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ding, X. P. Perturbed proximal point algorithm for generalized quasi-variational inclusions. J. Math. Anal. Appl. 210(1), 88–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ding, X. P. On a class of generalized nonlinear implicit quasi-variational inclusions. Appl. Math. Mech. (Engl. Ed.) 20(10), 1087–1098 (1999) DOI 10.1007/BF02460325

    Article  MATH  Google Scholar 

  6. Ding, X. P. Perturbed Ishikawa type iterative algorithm for generalized quasi-variational inclusions. Appl. Math. Comput. 141(1), 359–373 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fang, Y. P. and Huang, N. J. H-monotone operator and resolvent operator technique for variational inclusions. Appl. Math. Comput. 145(3), 795–803 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ding, Y. P. Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions. Appl. Math. Lett. 17(2), 225–235 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ding. X. P. and Yao J. C. Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces. Comput. Math. Appl. 49(5–6), 857–869 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ding, X. P. Predictor-corrector iterative algorithms for solving generalized mixed quasi-variationallike inclusion. J. Comput. Appl. Math. 182(1), 1–12 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ding, X. P. Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings. J. Comput. Appl. Math. 182(2), 252–269 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mordukhovich, B. S. Variational Analysis and Generalized Differentiation, Vols. I and II, Springer-Verlag, New York (2006)

    Google Scholar 

  13. Lin, L. J. Systems of generalized quasi-variational inclusions problems with applications to variational analysis and optimization problems. J. Glob. Optim. 38(1), 21–39 (2007)

    Article  MATH  Google Scholar 

  14. Lin, L. J. and Tu, C. I. The studies of systems of variational inclusions problems and applications. Nonlinear Anal. 69(7), 1981–1987 (2007)

    MathSciNet  Google Scholar 

  15. Ding. X. P. Maximal elements of a family of G B-majorized mappings in product FC-spaces and applications. Appl. Math. Mech. (Engl. Ed.) 27(12), 1607–1618 (2006) DOI 10.1007/s10483-006-1203-1

    Article  MATH  Google Scholar 

  16. Ding, X. P. Maximal elements of G KKM-majorized mappings in product FC-spaces and applications (I). Nonlinear Anal. 67(3), 963–973 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ben-El-Mechaiekh, H., Chebbi, S., Flornzano, M., and Llinares, J. V. Abstract convexity and fixed points. J. Math. Anal. Appl. 222(1), 138–150 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ding. X. P. Maximal element theorems in product FC-spaces and generalized games. J. Math. Anal. Appl. 305(1), 29–42 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Horvath, C. D. Contractibility and generalized convexity. J. Math. Anal. Appl. 156(2), 341–357 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  20. Park, S. and Kim, H. Foundations of the KKM theory on generalized convex spaces. J. Math. Anal. Appl. 209(3), 551–571 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    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  (丁协平)

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

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xie-ping Ding  (丁协平).

Additional information

Contributed by Xie-ping DING

Project supported by the Scientific Research Fund of Sichuan Normal University (No. 09ZDL04) 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 quasi-variational inclusion (disclusion) problems in FC-spaces. Appl. Math. Mech.-Engl. Ed. 31, 545–556 (2010). https://doi.org/10.1007/s10483-010-0502-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-010-0502-x

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation