IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v146y2010i3d10.1007_s10957-010-9690-5.html
   My bibliography  Save this article

Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems

Author

Listed:
  • P. Q. Khanh

    (International University of Hochiminh City)

  • N. H. Quan

    (Information Technology College of Hochiminh City)

Abstract

Applying generalized KKM-type theorems established in our previous paper (Khanh et al. in Nonlinear Anal. 71:1227–1234, 2009), we prove the existence of solutions to a general variational inclusion problem, which contains most of the existing results of this type. As applications, we obtain minimax theorems in various settings and saddle-point theorems in particular. Examples are given to explain advantages of our results.

Suggested Citation

  • P. Q. Khanh & N. H. Quan, 2010. "Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 640-653, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9690-5
    DOI: 10.1007/s10957-010-9690-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9690-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9690-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    2. P. Q. Khanh & L. M. Luu, 2004. "On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 533-548, December.
    3. L. J. Lin & W. P. Wan, 2004. "KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 105-122, October.
    4. G. M. Lee & S. H. Kum, 2000. "On Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 409-425, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. P. Q. Khanh & N. H. Quan, 2011. "Generic Stability and Essential Components of Generalized KKM Points and Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 488-504, March.
    2. P. Q. Khanh & V. S. T. Long & N. H. Quan, 2011. "Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 552-572, December.
    3. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.
    2. M. Fakhar & M. Lotfipour & J. Zafarani, 2013. "On the Brézis Nirenberg Stampacchia-type theorems and their applications," Journal of Global Optimization, Springer, vol. 55(4), pages 751-770, April.
    3. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    4. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    5. Phan Khanh & Lai Lin & Vo Long, 2014. "On topological existence theorems and applications to optimization-related problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 253-272, June.
    6. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.
    7. L. Q. Anh & P. Q. Khanh & D. T. M. Van, 2012. "Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 42-59, April.
    8. R. P. Agarwal & M. Balaj & D. O’Regan, 2012. "A Unifying Approach to Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 417-429, November.
    9. L. Anh & A. Kruger & N. Thao, 2014. "On Hölder calmness of solution mappings in parametric equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 331-342, April.
    10. X. P. Ding & J. Y. Park, 2004. "Generalized Vector Equilibrium Problems in Generalized Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 327-353, February.
    11. L. Q. Anh & P. Q. Khanh, 2009. "Hölder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 37-54, April.
    12. M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    13. Xu, Y.D. & Li, S.J. & Teo, K.L., 2012. "Vector network equilibrium problems with capacity constraints of arcs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 567-577.
    14. Mircea Balaj, 2011. "Alternative principles and their applications," Journal of Global Optimization, Springer, vol. 50(3), pages 537-547, July.
    15. L. Anh & P. Khanh & T. Tam, 2015. "On Hölder continuity of solution maps of parametric primal and dual Ky Fan inequalities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 151-167, April.
    16. S. Al-Homidan & Q. H. Ansari & S. Schaible, 2007. "Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 515-531, September.
    17. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    18. P. Q. Khanh & L. T. Tung, 2012. "Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 840-854, December.
    19. M.H. Kim & S.H. Kum & G.M. Lee, 2002. "Vector Variational Inequalities Involving Vector Maximal Points," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 593-607, September.
    20. P. Q. Khanh & N. H. Quan, 2011. "Generic Stability and Essential Components of Generalized KKM Points and Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 488-504, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9690-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.