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Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions 1

Author

Listed:
  • M. Fakhar

    (University of Isfahan)

  • J. Zafarani

    (University of Isfahan)

Abstract

In this paper, we apply a new version of the Brézis, Nirenberg, and Stampacchia theorem; we use pseudomonotonicity and some coercivity conditions to establish some existence result for a solution of generalized vector equilibrium problems for multivalued bifunctions. The proper quasiconvexity of multivalued bifunctions is introduced and existence theorems for generalized vector equilibrium problems related to multivalued mappings with the KKM property are obtained. The new results extend and modify various existence theorems for similar problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:1:d:10.1007_s10957-005-2663-4
    DOI: 10.1007/s10957-005-2663-4
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    Cited by:

    1. M. Fakhar & M. Lotfipour & J. Zafarani, 2013. "On the Brézis Nirenberg Stampacchia-type theorems and their applications," Journal of Global Optimization, Springer, vol. 55(4), pages 751-770, April.
    2. M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    3. T. Jabarootian & J. Zafarani, 2008. "Generalized Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 15-30, January.

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