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Existence of equilibria for monotone multivalued mappings

Author

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  • Werner Oettli
  • Dirk Schläger

Abstract

Using a particular kind of pseudomonotonicity for multivalued mappings, an existence result is proved for equilibria, variational inequalities, and a combination of both. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:219-228
    DOI: 10.1007/s001860050024
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    Citations

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    Cited by:

    1. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    2. X. P. Ding & J. Y. Park, 2004. "Generalized Vector Equilibrium Problems in Generalized Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 327-353, February.
    3. 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.
    4. 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.
    5. G. Y. Chen & X. Q. Yang, 2002. "Characterizations of Variable Domination Structures via Nonlinear Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 97-110, January.
    6. M. Fakhar & J. Zafarani, 2008. "Generalized Symmetric Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 397-409, March.
    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. 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.
    9. 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.
    10. Pham Huu Sach, 2018. "Solution Existence in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 1-16, January.
    11. Gábor Kassay & Mihaela Miholca & Nguyen The Vinh, 2016. "Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 424-442, May.

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