IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v155y2012i2d10.1007_s10957-012-0090-x.html
   My bibliography  Save this article

A Unifying Approach to Variational Relation Problems

Author

Listed:
  • R. P. Agarwal

    (Texas A&M University, Kingsville)

  • M. Balaj

    (University of Oradea)

  • D. O’Regan

    (National University of Ireland)

Abstract

The purpose of this paper is to present a unified approach to study the existence of solutions for two types of variational relation problems, which encompass several generalized equilibrium problems, variational inequalities and variational inclusions investigated in the recent literature. By using two well-known fixed point theorems, we establish several existence criteria for the solutions of these problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0090-x
    DOI: 10.1007/s10957-012-0090-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0090-x
    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/s10957-012-0090-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. 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. 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.
    3. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    4. 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.
    5. P. Cubiotti, 1997. "Generalized Quasi-Variational Inequalities Without Continuities," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 477-495, March.
    6. M. Balaj & L. J. Lin, 2011. "Generalized Variational Relation Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 1-13, January.
    7. 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.
    8. 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.
    9. 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.
    10. G. M. Lee & S. H. Kum, 2000. "On Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 409-425, February.
    11. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    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. Anulekha Dhara & Dinh Luc, 2014. "A solution method for linear variational relation problems," Journal of Global Optimization, Springer, vol. 59(4), pages 729-756, August.
    2. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. R. P. Agarwal & M. Balaj & D. O’Regan, 2014. "A Common Fixed Point Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 482-490, November.
    7. M. Balaj & L. J. Lin, 2011. "Generalized Variational Relation Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 1-13, January.
    8. 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.
    9. 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.
    10. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.
    11. 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.
    12. Zhe Yang & Yong Jian Pu, 2012. "Generalized Knaster–Kuratowski–Mazurkiewicz Theorem Without Convex Hull," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 17-29, July.
    13. 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.
    14. Anulekha Dhara & Dinh Luc, 2014. "A solution method for linear variational relation problems," Journal of Global Optimization, Springer, vol. 59(4), pages 729-756, August.
    15. Raúl Fierro, 2021. "An Intersection Theorem for Topological Vector Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 118-133, October.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Phan Khanh & Lai Lin & Vo Long, 2014. "On topological existence theorems and applications to optimization-related problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 253-272, June.

    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:155:y:2012:i:2:d:10.1007_s10957-012-0090-x. 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.