IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v184y2020i3d10.1007_s10957-019-01629-1.html
   My bibliography  Save this article

Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities

Author

Listed:
  • Bijaya Kumar Sahu

    (Indian Institute of Technology Bhubaneswar)

  • Ouayl Chadli

    (Ibn Zohr University)

  • Ram N. Mohapatra

    (University of Central Florida)

  • Sabyasachi Pani

    (Indian Institute of Technology Bhubaneswar)

Abstract

In this paper, we study the existence of solutions for mixed equilibrium problems associated with a set-valued operator in the general setting of vector spaces in duality, and in particular in Banach spaces. We use a Galerkin-type method and the notion of pseudomonotonicity in the sense of Brézis for bifunctions. As application, we study the existence of solutions for quasi-hemivariational inequalities governed by a set-valued mapping and perturbed with a nonlinear term. Our main results can be applied to differential inclusions, evolution equations and evolution hemivariational inequalities.

Suggested Citation

  • Bijaya Kumar Sahu & Ouayl Chadli & Ram N. Mohapatra & Sabyasachi Pani, 2020. "Existence Results for Mixed Equilibrium Problems Involving Set-Valued Operators with Applications to Quasi-Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 810-823, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01629-1
    DOI: 10.1007/s10957-019-01629-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01629-1
    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/s10957-019-01629-1?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. Daniel Steck, 2019. "Brezis Pseudomonotonicity is Strictly Weaker than Ky–Fan Hemicontinuity," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 318-323, April.
    2. 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.
    3. 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.
    4. Ouayl Chadli & Qamrul Hasan Ansari & Jen-Chih Yao, 2016. "Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 410-440, February.
    5. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    6. Nicuşor Costea & Vicenţiu Rădulescu, 2012. "Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term," Journal of Global Optimization, Springer, vol. 52(4), pages 743-756, April.
    7. Y. L. Zhang & Y. R. He, 2013. "The Hemivariational Inequalities for an Upper Semicontinuous Set-valued Mapping," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 716-725, March.
    8. O. Chadli & S. Schaible & J. C. Yao, 2004. "Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 571-596, June.
    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. M. Bianchi & G. Kassay & R. Pini, 2022. "Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization," Journal of Global Optimization, Springer, vol. 82(3), pages 483-498, March.
    2. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.
    3. Ouayl Chadli & Qamrul Hasan Ansari & Jen-Chih Yao, 2016. "Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 410-440, February.
    4. Giancarlo Bigi & Massimo Pappalardo & Mauro Passacantando, 2016. "Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 887-905, December.
    5. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    6. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    7. Pineda, Salvador & Boomsma, Trine K. & Wogrin, Sonja, 2018. "Renewable generation expansion under different support schemes: A stochastic equilibrium approach," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1086-1099.
    8. Cholamjiak, Watcharaporn & Dutta, Hemen & Yambangwai, Damrongsak, 2021. "Image restorations using an inertial parallel hybrid algorithm with Armijo linesearch for nonmonotone equilibrium problems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. Habib ur Rehman & Wiyada Kumam & Kamonrat Sombut, 2022. "Inertial Modification Using Self-Adaptive Subgradient Extragradient Techniques for Equilibrium Programming Applied to Variational Inequalities and Fixed-Point Problems," Mathematics, MDPI, vol. 10(10), pages 1-29, May.
    10. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.
    11. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    12. Mostafa Nasri & Luiz Carlos Matioli & Euda Mara Silva Ferreira & Adilson Silveira, 2016. "Implementation of Augmented Lagrangian Methods for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 971-991, March.
    13. Riccardi, R. & Bonenti, F. & Allevi, E. & Avanzi, C. & Gnudi, A., 2015. "The steel industry: A mathematical model under environmental regulations," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1017-1027.
    14. 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.
    15. Yekini Shehu & Lulu Liu & Xiaolong Qin & Qiao-Li Dong, 2022. "Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models," Networks and Spatial Economics, Springer, vol. 22(1), pages 153-180, March.
    16. 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.
    17. Uthai Kamraksa & Rabian Wangkeeree, 2011. "Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 689-714, December.
    18. Thi Thu Van Nguyen & Jean Jacques Strodiot & Van Hien Nguyen, 2014. "Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 809-831, March.
    19. Giancarlo Bigi & Mauro Passacantando, 2015. "Descent and Penalization Techniques for Equilibrium Problems with Nonlinear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 804-818, March.
    20. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, 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:184:y:2020:i:3:d:10.1007_s10957-019-01629-1. 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.