IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1604-d415000.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this article

Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

Author

Listed:
  • Jing-Nan Li

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • San-Hua Wang

    (Department of Mathematics, Nanchang University, Nanchang 330031, China
    Post-Doctor Station of Management Science and Engineering, Nanchang University, Nanchang 330031, China)

  • Yu-Ping Xu

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

Abstract

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1604-:d:415000
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1604/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1604/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. X. Gong, 2007. "Symmetric strong vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 305-314, April.
    3. 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.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. 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.
    6. 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.
    7. 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)

    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. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. X. Gong, 2007. "Symmetric strong vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 305-314, April.
    9. M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    10. 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.
    11. 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.
    12. L. J. Lin & H. J. Shie, 2008. "Existence Theorems of Quasivariational Inclusion Problems with Applications to Bilevel Problems and Mathematical Programs with Equilibrium Constraint," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 445-457, September.
    13. Agnieszka Kurdyś-Kujawska & Agnieszka Sompolska-Rzechuła & Joanna Pawłowska-Tyszko & Michał Soliwoda, 2021. "Crop Insurance, Land Productivity and the Environment: A Way forward to a Better Understanding," Agriculture, MDPI, vol. 11(11), pages 1-17, November.
    14. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.
    15. Wenfeng Chi & Yuanyuan Zhao & Wenhui Kuang & Tao Pan & Tu Ba & Jinshen Zhao & Liang Jin & Sisi Wang, 2021. "Impact of Cropland Evolution on Soil Wind Erosion in Inner Mongolia of China," Land, MDPI, vol. 10(6), pages 1-16, June.
    16. Yulin Zhao, 2012. "Positive Solutions for ( k , n − k ) Conjugate Multipoint Boundary Value Problems in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, August.
    17. Nick Middleton & Utchang Kang, 2017. "Sand and Dust Storms: Impact Mitigation," Sustainability, MDPI, vol. 9(6), pages 1-22, June.
    18. Tarantino, Emanuele & Pavanini, Nicola & Mayordomo, Sergio, 2020. "The Impact of Alternative Forms of Bank Consolidation on Credit Supply and Financial Stability," CEPR Discussion Papers 15069, C.E.P.R. Discussion Papers.
    19. Truong Duong & Nguyen Tan, 2012. "On the existence of solutions to generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 52(4), pages 711-728, April.
    20. Misbah Haque & Imran Ali, 2016. "Uncertain Environment and Organizational Performance: The Mediating Role of Organizational Innovation," Asian Social Science, Canadian Center of Science and Education, vol. 12(9), pages 124-124, 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:gam:jmathe:v:8:y:2020:i:9:p:1604-:d:415000. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.