IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v139y2008i1d10.1007_s10957-008-9429-8.html
   My bibliography  Save this article

Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems

Author

Listed:
  • X. H. Gong

    (Nanchang University)

Abstract

In this paper, we obtain some stability results for parametric weak vector equilibrium problems in topological vector spaces. We provide sufficient conditions for the continuity of the solution set mapping in parametric weak monotone vector equilibrium problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9429-8
    DOI: 10.1007/s10957-008-9429-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9429-8
    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/s10957-008-9429-8?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. 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. 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.
    3. 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.
    4. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    5. 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.
    6. E. Muselli, 2000. "Upper and Lower Semicontinuity for Set-Valued Mappings Involving Constraints," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 527-550, September.
    7. 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.
    8. Q. Ansari & W. Oettli & D. Schläger, 1997. "A generalization of vectorial equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 147-152, June.
    9. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    10. Y. Chiang & O. Chadli & J. Yao, 2004. "Generalized Vector Equilibrium Problems with Trifunctions," Journal of Global Optimization, Springer, vol. 30(2), pages 135-154, November.
    11. Jun-Yi Fu, 2000. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 57-64, September.
    12. 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.
    13. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    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 & 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.
    3. 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.
    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. 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.
    6. 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.
    7. Li, X.B. & Li, S.J., 2014. "Hölder continuity of perturbed solution set for convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 908-918.
    8. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    9. 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.
    10. X. Gong, 2011. "Chebyshev scalarization of solutions to the vector equilibrium problems," Journal of Global Optimization, Springer, vol. 49(4), pages 607-622, April.
    11. 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.
    12. Pham Huu Sach & Le Anh Tuan, 2013. "New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 347-364, May.
    13. 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.
    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.

    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. 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.
    2. 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.
    3. 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.
    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. 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.
    6. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    7. 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.
    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. 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.
    10. 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.
    11. Jian-Wen Peng & Soon-Yi Wu & Yan Wang, 2012. "Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints," Journal of Global Optimization, Springer, vol. 52(4), pages 779-795, April.
    12. Wensheng Jia & Xiaoling Qiu & Dingtao Peng, 2020. "An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    13. 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.
    14. 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.
    15. Tran Van Su, 2018. "New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces," 4OR, Springer, vol. 16(2), pages 173-198, June.
    16. Junyi Fu & Sanhua Wang, 2013. "Generalized strong vector quasi-equilibrium problem with domination structure," Journal of Global Optimization, Springer, vol. 55(4), pages 839-847, April.
    17. 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.
    18. 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.
    19. Szilárd László, 2016. "Vector Equilibrium Problems on Dense Sets," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 437-457, August.
    20. Jing-Nan Li & San-Hua Wang & Yu-Ping Xu, 2020. "Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures," Mathematics, MDPI, vol. 8(9), pages 1-17, September.

    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:139:y:2008:i:1:d:10.1007_s10957-008-9429-8. 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.