Advertisement

Applied Mathematics and Mechanics

, Volume 31, Issue 5, pp 545–556 | Cite as

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

  • Xie-ping Ding (丁协平)Email author
Article
  • 27 Downloads

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.

Key words

maximal element system of generalized quasi-variational inclusion (disclusion) problems partially diagonallyquasi-convex partially diagonally quasi-concave FC-space 

Chinese Library Classification

O176.3 O177.92 

2000 Mathematics Subject Classification

49J27 49J40 49J53 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Robinson, S. M. Generalized equation and their solutions, part I: basic theory. Math. Program. Study 10(1), 128–141 (1979)zbMATHGoogle Scholar
  2. [2]
    Hassouni, A. and Moudafi, A. A perturbed algorithm for variational inclusions. J. Math. Anal. Appl. 185(3), 706–721 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Adly, S. Perturbed algorithms and sensitivity analysis for a general class of variational inclusions. J. Math. Anal. Appl. 201(3), 609–630 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Ding, X. P. Perturbed proximal point algorithm for generalized quasi-variational inclusions. J. Math. Anal. Appl. 210(1), 88–101 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [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/BF02460325zbMATHCrossRefGoogle Scholar
  6. [6]
    Ding, X. P. Perturbed Ishikawa type iterative algorithm for generalized quasi-variational inclusions. Appl. Math. Comput. 141(1), 359–373 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [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)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Ding, Y. P. Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions. Appl. Math. Lett. 17(2), 225–235 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  9. [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)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Ding, X. P. Predictor-corrector iterative algorithms for solving generalized mixed quasi-variationallike inclusion. J. Comput. Appl. Math. 182(1), 1–12 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. [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)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Mordukhovich, B. S. Variational Analysis and Generalized Differentiation, Vols. I and II, Springer-Verlag, New York (2006)Google Scholar
  13. [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)zbMATHCrossRefGoogle Scholar
  14. [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)MathSciNetGoogle Scholar
  15. [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/s10483-006-1203-1zbMATHCrossRefGoogle Scholar
  16. [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)zbMATHCrossRefMathSciNetGoogle Scholar
  17. [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)zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Ding. X. P. Maximal element theorems in product FC-spaces and generalized games. J. Math. Anal. Appl. 305(1), 29–42 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    Horvath, C. D. Contractibility and generalized convexity. J. Math. Anal. Appl. 156(2), 341–357 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    Park, S. and Kim, H. Foundations of the KKM theory on generalized convex spaces. J. Math. Anal. Appl. 209(3), 551–571 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    Aubin, J. P. and Ekeland, I. Applied Nonlinear Analysis, John Wiley and Sons, New York (1984)zbMATHGoogle Scholar
  22. [22]
    Aliprantis, C. D. and Border, K. C. Infinite Dimensional Analysis, Springer-Verlag, New York (1994)zbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityChengduP. R. China

Personalised recommendations