IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i1d10.1007_s10957-007-9222-0.html
   My bibliography  Save this article

Systems of Set-Valued Quasivariational Inclusion Problems

Author

Listed:
  • N. X. Hai

    (Posts and Telecommunications Institute of Technology)

  • P. Q. Khanh

    (International University of Hochiminh City)

Abstract

We propose four kinds of systems of set-valued quasivariational inclusion problems in product spaces, which include many known systems of equilibrium problems and systems of variational inequalities as well as inclusion problems. Sufficient conditions for the solution existence are established. When applied to special cases, these conditions improve many existing results in the literature. To ensure the generality of our problem setting and results, applications in fixed-point theory and quasioptimization problems are included.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:1:d:10.1007_s10957-007-9222-0
    DOI: 10.1007/s10957-007-9222-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9222-0
    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/s10957-007-9222-0?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. 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.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    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. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    7. Angelo Guerraggio & Nguyen Xuan Tan, 2002. "On general vector quasi-optimization problems," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 347-358, June.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    9. L. J. Lin & Z. T. Yu & G. Kassay, 2002. "Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 189-208, July.
    10. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    12. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    13. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    14. 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.
    15. 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.
    16. Angelo Guerraggio & Nguyen Xuan Tan, 2002. "On general vector quasi-optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 347-358, June.
    17. B. Djafari. Rouhani & E. Tarafdar & P. J. Watson, 2005. "Existence of Solutions to Some Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 97-107, July.
    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. 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.
    2. Ali Farajzadeh & Byung Soo Lee & Somyot Plubteing, 2016. "On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 584-599, February.
    3. P. H. Sach & L. J. Lin & L. A. Tuan, 2010. "Generalized Vector Quasivariational Inclusion Problems with Moving Cones," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 607-620, December.

    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. 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.
    2. Youwei Zhang, 2014. "Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces," International Journal of Analysis, Hindawi, vol. 2014, pages 1-18, May.
    3. Maloni, Michael & Jackson, Eric C., 2005. "North American Container Port Capacity," 46th Annual Transportation Research Forum, Washington, D.C., March 6-8, 2005 208147, Transportation Research Forum.
    4. T. Jankowski & R. Jankowski, 2010. "Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 105-115, July.
    5. Jeongmi Jeong & Chan-Gyun Kim, 2020. "Existence of Positive Solutions to Singular φ -Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    6. C.V.O. Eneji & E. Obim & J.E.O. Eneji & T.O. Ellah & A. Ushie, 2013. "Civil Societies/Non- Governmental Organizations as Catalysts for the Attainment of the Millennium Development Goals in Nigeria," International Journal of Management Sciences, Research Academy of Social Sciences, vol. 1(11), pages 427-435.
    7. Ehsan Pourhadi & Reza Saadati & Sotiris K. Ntouyas, 2019. "Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    8. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    10. Christopher S. Goodrich, 2021. "A topological approach to nonlocal elliptic partial differential equations on an annulus," Mathematische Nachrichten, Wiley Blackwell, vol. 294(2), pages 286-309, February.
    11. Götz Alefeld & Zhengyu Wang, 2011. "Error Bounds for Nonlinear Complementarity Problems with Band Structure," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 33-51, July.
    12. Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, June.
    13. Li, Qiang & Li, Yongxiang, 2015. "Monotone iterative technique for second order delayed periodic problem in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 654-664.
    14. 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.
    15. Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.
    16. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    17. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    18. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    19. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    20. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.

    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:135:y:2007:i:1:d:10.1007_s10957-007-9222-0. 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.