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On Vector Quasi-Equilibrium Problems with Set-Valued Maps

Author

Listed:
  • S. H. Hou

    (Hong Kong Polytechnic University)

  • H. Yu

    (Institute of Systems Science)

  • G. Y. Chen

    (Institute of Systems Science)

Abstract

In this paper, we introduce a new class of vector quasi-equilibrium problems with set-valued maps. Almost all the vector equilibrium models of the Blum-Oettli type in the literature are special cases of our new class of equilibrium problems under consideration. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the γ-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for such vector equilibrium problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006686.19635.ad
    DOI: 10.1023/B:JOTA.0000006686.19635.ad
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    References listed on IDEAS

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    1. Werner Oettli & Dirk Schläger, 1998. "Existence of equilibria for monotone multivalued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 219-228, November.
    2. Guoqiang Tian, 1993. "Generalized Quasi-Variational-Like Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 752-764, August.
    3. Q. Ansari & W. Oettli & D. Schläger, 1997. "A generalization of vectorial equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 147-152, June.
    4. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    5. S. Park, 1997. "Generalized Equilibrium Problems and Generalized Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 409-417, November.
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    Citations

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    Cited by:

    1. Lai-Jiu Lin & Qamrul Ansari & Yu-Jen Huang, 2007. "Some existence results for solutions of generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 85-98, February.
    2. 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.
    3. L. J. Lin & Y. H. Liu, 2006. "Existence Theorems for Systems of Generalized Vector Quasiequilibrium Problems and Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 463-477, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. G. Mastroeni, 2012. "On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation," Journal of Global Optimization, Springer, vol. 53(2), pages 203-214, June.

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