Necessary conditions for two-function minimax inequalities

  • Ferenc Forgó
  • István Joó
Part of the Applied Optimization book series (APOP, volume 13)


Necessary conditions are given for the two-function minimax inequality to hold for a large family of subsets of the sets involved. The functions should belong to a class consisting of certain generalizations of convex (concave)-like functions. Most of the analysis takes place in topological vector spaces but the results are also extended to pseudoconvex spaces.


Variational Inequality Topological Vector Space Minimax Theorem Hausdorff Topological Vector Space Compact Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berge,C., Topological spaces, Macmillan, New York, (1963).zbMATHGoogle Scholar
  2. 2.
    Browder, F. E., The fixed point theory of multivalued mappings in topological vector spaces, Math. Ann. 177 (1968), 283–302.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Forg, F. and Joô, I., Necessary conditions for maxmin=minmax, to appear in Acta Math. Acad. Sci. Hung. (1996).Google Scholar
  4. 4.
    Joô, I. and KASSAY, G., Convexity, minimax theorems and their applications, Annales Univ. Sci. Budapest Sect. Math. 38 (1995), 71–93.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Joô, I., On some convexities, Acta Math. Hung. 54 (1989), 163–172.CrossRefzbMATHGoogle Scholar
  6. 6.
    Kindler, J., Intersection theorems and minimax theorems based on connectedness, J. Math. Anal. Appl. 178 (1993) 529–546.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Martos, B., Nonlinear programming theory and methods, Akadémiai Kiadô, Budapest, (1975).zbMATHGoogle Scholar
  8. 8.
    Simons, S., Criteres de faible compacite en termes du théoreme de minimax,Seminaire Choquet 1970/71, no. 23, 8 pages.Google Scholar
  9. 9.
    Simons, S., Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, Proceedings of Symposia in Pure Mathematics, 45 (1986), Part 2, 377–392.Google Scholar
  10. 10.
    Simons, S., Minimax theorems and their proofs, in: Minimax and Applications ed. Ding-Zhu Du and Panos M. Pardalos, Kluwer Academic Publishers, Boston, 1995, 1–23.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Ferenc Forgó
    • 1
  • István Joó
    • 2
  1. 1.Department of Operations ResearchBudapest University of Economic SciencesBudapestHungary
  2. 2.Eötvös Loránd UniversityBudapestHungary

Personalised recommendations