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Generalized Symmetric Vector Quasiequilibrium Problems

Author

Listed:
  • M. Fakhar

    (University of Isfahan
    Institute for Studies in Theoretical Physics and Mathematics (IPM))

  • J. Zafarani

    (University of Isfahan and Sheikhbahaee University)

Abstract

We establish an existence result for scalar quasiequilibrium problems without any continuity requirement on noncompact subsets of locally convex topological vector spaces. As a consequence, we obtain a solution of symmetric scalar quasiequilibrium problem. Moreover, using a so-called nonlinear scalarization function, existence theorems for vector quasiequilibrium problems and general symmetric vector quasiequilibrium problems are obtained.

Suggested Citation

  • M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:3:d:10.1007_s10957-007-9310-1
    DOI: 10.1007/s10957-007-9310-1
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    References listed on IDEAS

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    1. M. Fakhar & J. Zafarani, 2005. "Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions 1," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 109-124, July.
    2. 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.
    3. P. Cubiotti, 1997. "Generalized Quasi-Variational Inequalities Without Continuities," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 477-495, March.
    4. P. Q. Khanh & L. M. Luu, 2004. "On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 533-548, December.
    5. M. Fakhar & J. Zafarani, 2005. "Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 125-136, July.
    6. Jen-Chih Yao, 1995. "Generalized-Quasi-Variational Inequality Problems with Discontinuous Mappings," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 465-478, May.
    7. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    8. 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.
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    Cited by:

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