IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i2d10.1007_s10957-007-9250-9.html
   My bibliography  Save this article

On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems

Author

Listed:
  • L. Q. Anh

    (Cantho University)

  • P. Q. Khanh

    (International University of Hochiminh City)

Abstract

We give sufficient conditions for the semicontinuity of solution sets of general multivalued vector quasiequilibrium problems. All kinds of semicontinuities are considered: lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity, and closedness. Moreover, we investigate the weak, middle, and strong solutions of quasiequilibrium problems. Many examples are provided to give more insights and comparisons with recent existing results.

Suggested Citation

  • L. Q. Anh & P. Q. Khanh, 2007. "On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 271-284, November.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9250-9
    DOI: 10.1007/s10957-007-9250-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9250-9
    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/s10957-007-9250-9?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. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    2. Jun-Yi Fu & An-Hua Wan, 2002. "Generalized vector equilibrium problems with set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 259-268, November.
    3. P. Q. Khanh & L. M. Luu, 2007. "Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 329-339, June.
    4. 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.
    5. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    6. L. J. Lin & Z. T. Yu & G. Kassay, 2002. "Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 189-208, July.
    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. Ren-you Zhong & Nan-jing Huang, 2011. "Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 317-326, August.
    2. S. J. Li & X. B. Li, 2011. "Hölder Continuity of Solutions to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 540-553, June.
    3. S. J. Li & Z. M. Fang, 2010. "Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 507-515, December.
    4. Lam Anh & Phan Khanh, 2010. "Continuity of solution maps of parametric quasiequilibrium problems," Journal of Global Optimization, Springer, vol. 46(2), pages 247-259, February.
    5. 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.
    6. Júlia Salamon, 2010. "Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 173-183, June.
    7. 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.
    8. Ren-you Zhong & Nan-jing Huang, 2011. "Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 564-579, June.
    9. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.
    10. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    11. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    12. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.
    13. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    14. 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.
    15. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.

    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. 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.
    2. Lam Anh & Phan Khanh, 2010. "Continuity of solution maps of parametric quasiequilibrium problems," Journal of Global Optimization, Springer, vol. 46(2), pages 247-259, February.
    3. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.
    4. 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.
    5. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    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. 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.
    8. P. H. Sach, 2008. "On a Class of Generalized Vector Quasiequilibrium Problems with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 337-350, November.
    9. Ren-you Zhong & Nan-jing Huang, 2011. "Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 317-326, August.
    10. P. H. Sach & L. A. Tuan, 2007. "Existence Results for Set-Valued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 229-240, May.
    11. Xing Wang & Nan-Jing Huang, 2013. "Differential Vector Variational Inequalities in Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 109-129, July.
    12. Mircea Balaj, 2021. "Intersection theorems for generalized weak KKM set‐valued mappings with applications in optimization," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1262-1276, July.
    13. Ayed E. Hashoosh & Mohsen Alimohammady & M. K. Kalleji, 2016. "Existence Results for Some Equilibrium Problems Involving -Monotone Bifunction," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-5, February.
    14. L. J. Lin & Y. H. Liu, 2006. "Existence Theorems for Systems of Generalized Vector Quasiequilibrium Problems and Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 463-477, September.
    15. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.
    16. Massimiliano Giuli, 2013. "Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 130-144, July.
    17. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.
    18. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.
    19. S. Li & H. Liu & Y. Zhang & Z. Fang, 2013. "Continuity of the solution mappings to parametric generalized strong vector equilibrium problems," Journal of Global Optimization, Springer, vol. 55(3), pages 597-610, March.
    20. N. X. Tan, 2004. "On the Existence of Solutions of Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 619-638, December.

    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:135:y:2007:i:2:d:10.1007_s10957-007-9250-9. 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.