IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v269y2018i1d10.1007_s10479-017-2506-3.html
   My bibliography  Save this article

Solution of a class of equilibrium problems and variational inequalities in FC spaces

Author

Listed:
  • Gayatri Pany

    (IIT)

  • Ram N. Mohapatra

    (University of Central Florida)

  • Sabyasachi Pani

    (IIT)

Abstract

In this paper, we study a class of mixed variational-like inequalities with respect to generalized weakly relaxed $$\eta {-}\alpha $$ η - α monotone mappings, involving nonlinear bifunctions, in finitely continuous topological space, in short FC space. Existence of the solution to the problem is established relaxing convexity and linearity condition by using generalized RKKM theorem. We have proposed a proximal iterative scheme using auxiliary principle technique. Solvability of the auxiliary variational inequality problem is established. Finally convergence of the iterates to the exact solution is proved. Some results with application to equilibrium problem are also discussed.

Suggested Citation

  • Gayatri Pany & Ram N. Mohapatra & Sabyasachi Pani, 2018. "Solution of a class of equilibrium problems and variational inequalities in FC spaces," Annals of Operations Research, Springer, vol. 269(1), pages 565-582, October.
    • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2506-3
    DOI: 10.1007/s10479-017-2506-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-017-2506-3
    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/s10479-017-2506-3?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. Farajzadeh, A.P. & Plubtieng, S. & Ungchittrakool, K. & Kumtaeng, D., 2015. "Generalized mixed equilibrium problems with generalized α -η -monotone bifunction in topological vector spaces," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 313-319.
    2. Guoqiang Tian, 1993. "Generalized Quasi-Variational-Like Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 752-764, August.
    3. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    4. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    5. Ben-El-Mechaiekh, H. & Chebbi, S. & Florenzano, M. & Llinares, J.-V., 1997. "Abstract Convexity and Fixed Points," Papiers d'Economie Mathématique et Applications 97.87, Université Panthéon-Sorbonne (Paris 1).
    6. Y.P. Fang & N.J. Huang, 2003. "Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 327-338, August.
    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. G. C. Bento & J. X. Cruz Neto & P. A. Soares & A. Soubeyran, 2022. "A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires," Annals of Operations Research, Springer, vol. 316(2), pages 1301-1318, September.

    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. 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.
    2. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    3. 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.
    4. Xie Ding, 2010. "New systems of generalized vector quasi-equilibrium problems in product FC-spaces," Journal of Global Optimization, Springer, vol. 46(1), pages 133-146, January.
    5. Syed Shakaib Irfan & Mohammad Firdosh Khan, 2016. "Variational-Like Inequalities for Weakly Relaxed Pseudomonotone Set-Valued Mappings in Banach Space," International Journal of Analysis, Hindawi, vol. 2016, pages 1-6, September.
    6. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
    7. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.
    8. D. L. Zhu & L. L. Zhu & Q. Xu, 2008. "Generalized Invex Monotonicity and Its Role in Solving Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 453-464, May.
    9. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2008. "A generalization of Fan's matching theorem," PSE-Ecole d'économie de Paris (Postprint) hal-00756058, HAL.
    10. Llinarès, Juan Vicente, 1998. "Existence of equilibrium in generalized games with non-convex strategy spaces," CEPREMAP Working Papers (Couverture Orange) 9801, CEPREMAP.
    11. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2006. "A Generalization of Fan's Matching Theorem," Cahiers de la Maison des Sciences Economiques b06060a, Université Panthéon-Sorbonne (Paris 1), revised Jan 2008.
    12. S. K. Mishra & Vivek Laha, 2013. "On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 278-293, February.
    13. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    14. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.
    15. S. H. Hou & H. Yu & G. Y. Chen, 2003. "On Vector Quasi-Equilibrium Problems with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 485-498, December.
    16. M. Carmen Sánchez & Juan-Vicente Llinares & Begoña Subiza, 2003. "A KKM-result and an application for binary and non-binary choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 185-193, January.
    17. Pascal Gourdel & Hakim Hammami, 2007. "Applications of generalized Ky Fan's matching theorem in minimax and variational inequality," Post-Print halshs-00204627, HAL.
    18. Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.
    19. Nicuşor Costea & Daniel Alexandru Ion & Cezar Lupu, 2012. "Variational-Like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 79-99, October.
    20. Yu Zhang & Shih-Sen Chang & Tao Chen, 2021. "Existence and Generic Stability of Strong Noncooperative Equilibria of Vector-Valued Games," Mathematics, MDPI, vol. 9(24), pages 1-13, 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:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2506-3. 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.