A Note on König and Close Convexity in Minimax Theorems

  • Fernando Luque-Vásquez
  • J. Adolfo Minjárez-Sosa
  • Max E. Mitre-Báez


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.


König convexity Close convexity Minimax theorems 

Mathematics Subject Classification



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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Fernando Luque-Vásquez
    • 1
  • J. Adolfo Minjárez-Sosa
    • 1
  • Max E. Mitre-Báez
    • 1
  1. 1.Universidad de SonoraHermosilloMexico

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