A Note on König and Close Convexity in Minimax Theorems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)65-71
Number of pages7
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - 1 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.


  • Close convexity
  • König convexity
  • Minimax theorems


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