IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i4p1447-1464.html
   My bibliography  Save this article

Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces

Author

Listed:
  • Rabian Wangkeeree
  • Pakkapon Preechasilp

Abstract

In this paper, we establish some existence results for the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in reflexive Banach spaces. Using the concept of the stable $$f$$ -quasimonotonicity, the properties of Clarke’s generalized directional derivative, Clarke’s generalized gradient and KKM technique, some existence theorems of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Our main results extend various results existing in the current literatures. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1447-1464
    DOI: 10.1007/s10898-012-0018-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-0018-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-0018-x?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. D. T. Peng & J. Yu & N. H. Xiu, 2012. "Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 165-179, October.
    2. Zijia Peng & Zhenhai Liu, 2011. "Evolution hemivariational inequality problems with doubly nonlinear operators," Journal of Global Optimization, Springer, vol. 51(3), pages 413-427, November.
    3. 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.
    4. 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.
    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. 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.

    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. 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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Gasiński, Leszek & Migórski, Stanisław & Ochal, Anna & Peng, Zijia, 2018. "Optimal control for doubly nonlinear evolutionary inclusions," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 244-254.
    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.

    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:jglopt:v:57:y:2013:i:4:p:1447-1464. 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.