IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v147y2010i3d10.1007_s10957-010-9736-8.html
   My bibliography  Save this article

Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality

Author

Listed:
  • S. J. Li

    (Chongqing University)

  • Z. M. Fang

    (Chongqing University)

Abstract

In this paper, we investigate weak vector solutions and global vector solutions to a generalized Ky Fan inequality. Under new assumptions, which are weaker than the assumption of strict C-mappings, we establish the lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality by using a scalarization method. These results extend the corresponding ones in the literature. Some examples are given to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9736-8
    DOI: 10.1007/s10957-010-9736-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9736-8
    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/s10957-010-9736-8?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. 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.
    2. X. H. Gong, 2007. "Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 151-161, May.
    3. X. H. Gong & J. C. Yao, 2008. "Connectedness of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 189-196, August.
    4. X. H. Gong & J. C. Yao, 2008. "Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 197-205, August.
    5. S. H. Hou & X. H. Gong & X. M. Yang, 2010. "Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 387-398, August.
    6. 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.
    7. X. H. Gong, 2001. "Efficiency and Henig Efficiency for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 139-154, January.
    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. Rabian Wangkeeree & Pakkapon Preechasilp, 2013. "Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1447-1464, December.
    2. 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.
    3. Pham Sach & Nguyen Minh, 2013. "Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1401-1418, December.
    4. C. R. Chen & S. J. Li, 2013. "Semicontinuity Results on Parametric Vector Variational Inequalities with Polyhedral Constraint Sets," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 97-108, July.
    5. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    6. Z. Y. Peng & X. M. Yang & J. W. Peng, 2012. "On the Lower Semicontinuity of the Solution Mappings to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 256-264, January.

    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. X. Gong, 2011. "Chebyshev scalarization of solutions to the vector equilibrium problems," Journal of Global Optimization, Springer, vol. 49(4), pages 607-622, April.
    2. Adela Capătă, 2011. "Existence results for proper efficient solutions of vector equilibrium problems and applications," Journal of Global Optimization, Springer, vol. 51(4), pages 657-675, December.
    3. 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.
    4. 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.
    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. 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.
    7. Z. Y. Peng & X. M. Yang & J. W. Peng, 2012. "On the Lower Semicontinuity of the Solution Mappings to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 256-264, January.
    8. Qiuying Li & Sanhua Wang, 2021. "Arcwise Connectedness of the Solution Sets for Generalized Vector Equilibrium Problems," Mathematics, MDPI, vol. 9(20), pages 1-9, October.
    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. 149(3), pages 564-579, June.
    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. Yu Han & Nan-jing Huang, 2018. "Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 65-85, October.
    12. Yangdong Xu & Pingping Zhang, 2018. "Connectedness of Solution Sets of Strong Vector Equilibrium Problems with an Application," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 131-152, July.
    13. L. P. Hai & L. Huerga & P. Q. Khanh & V. Novo, 2019. "Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems," Journal of Global Optimization, Springer, vol. 74(2), pages 361-382, June.
    14. 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.
    15. 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.
    16. 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.
    17. Bin Chen & Nan-jing Huang, 2013. "Continuity of the solution mapping to parametric generalized vector equilibrium problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1515-1528, August.
    18. C. R. Chen & S. J. Li, 2013. "Semicontinuity Results on Parametric Vector Variational Inequalities with Polyhedral Constraint Sets," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 97-108, July.
    19. Zaiyun Peng & Ziyuan Wang & Xinmin Yang, 2020. "Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 188-206, April.
    20. X. H. Gong & J. C. Yao, 2008. "Connectedness of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 189-196, August.

    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:147:y:2010:i:3:d:10.1007_s10957-010-9736-8. 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.