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A Note on König and Close Convexity in Minimax Theorems

Author

Listed:
  • Fernando Luque-Vásquez

    (Universidad de Sonora)

  • J. Adolfo Minjárez-Sosa

    (Universidad de Sonora)

  • Max E. Mitre-Báez

    (Universidad de Sonora)

Abstract

We give an example of a real-valued function defined on the Cartesian product of two compact sets, which is König convex but not closely convex. Additionally, we prove that under suitable conditions, König convexity implies close convexity.

Suggested Citation

  • Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa & Max E. Mitre-Báez, 2016. "A Note on König and Close Convexity in Minimax Theorems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 65-71, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0922-1
    DOI: 10.1007/s10957-016-0922-1
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    References listed on IDEAS

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    1. J.F.B. Frenk & G. Kassay, 2002. "Minimax Results and Finite-Dimensional Separation," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 409-421, May.
    2. Frenk, J. B. G. & Kassay, G. & Kolumban, J., 2004. "On equivalent results in minimax theory," European Journal of Operational Research, Elsevier, vol. 157(1), pages 46-58, August.
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