Skip to main content
SpringerLink
Log in

On a minimax theorem of Terkelsen's

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C. Carlson, Algorithms involving arithmetic and geometric means. Amer. Math. Monthly78, 496–505 (1971).

    Google Scholar 

  2. D. A. Cox, The arithmetic-geometric mean of Gauss. Enseignement Math.30, 275–330 (1984).

    Google Scholar 

  3. B. C. Cuóng, Some remarks on minimax theorems. Acta Math. Vietnam.1, 67–74 (1976).

    Google Scholar 

  4. M. de Wilde, Doubles limites ordonnées et théorèmes de minimax. Ann. Inst. Fourier24, 181–188 (1974).

    Google Scholar 

  5. D.Dubois and H.Prade, Possibility theory. New York 1988.

  6. Ky Fan, Minimax theorems. Proc. Nat. Acad. Sci. USA39, 42–47 (1953).

    Google Scholar 

  7. D. M. E. Foster andG. M. Phillips, A generalization of the Archimedian double sequence. J. Math. Anal. Appl.101, 575–581 (1984).

    Google Scholar 

  8. D. M. E. Foster andG. M. Phillips, The arithmetic-harmonic mean. Math. Comp.42, 181–191 (1984).

    Google Scholar 

  9. M. A. Geraghty andB.-L. Lin, On a minimax theorem of Terkelsen. Bull. Inst. Math. Acad. Sinica11, 343–347 (1983). Correction:12, 203 (1984).

    Google Scholar 

  10. M. A. Geraghty andB.-L. Lin, Topological minimax theorems. Proc. Amer. Math. Soc.91, 377–380 (1984).

    Google Scholar 

  11. M. A. Geraghty andB.-L. Lin, Minimax theorems without linear structure. Linear and Multilinear Algebra17, 171–180 (1985).

    Google Scholar 

  12. M. A. Geraghty andB.-L. Lin, Minimax theorems without convexity. Contemporary Math.52, 102–108 (1986).

    Google Scholar 

  13. J. Hartung, An extension of Sion's minimax theorem with an application to a method for constrained games. Pacific J. Math.103, 401–408 (1982).

    Google Scholar 

  14. A.Irle, Minimax theorems in convex situations. In: Game theory and mathematical economics. Proceedings. O. Moeschlin and D. Pallaschke, Eds., Amsterdam-New York-Oxford 1981.

  15. A. Irle, A general minimax theorem. Z. Oper. Research29, 229–247 (1985).

    Google Scholar 

  16. A. Irle, On minimax theorems for hide-and-seek games. Methods Oper. Res.54, 373–383 (1986).

    Google Scholar 

  17. J. Kindler, Über Spiele auf konvexen Mengen. Methods Oper. Res.26, 695–704 (1977).

    Google Scholar 

  18. J. Kindler, Schwach definite Spiele. Math. Operationsforsch. Statist., Ser. Optimization8, 199–205 (1977).

    Google Scholar 

  19. J. Kindler andR. Trost, Minimax theorems for interval spaces. Acta Math. Hung.54, 39–49 (1989).

    Google Scholar 

  20. H. König, Über das von Neumannsche Minimax-Theorem. Arch. Math.19, 482–487 (1968).

    Google Scholar 

  21. H.König, Aufgabe 8 in: Mathematische Wirtschaftstheorie. Lecture Notes, Universität Karlsruhe 1977–1978.

  22. H.König, On some basic theorems in convex analysis. In: Modern applied mathematics-optimization and operations research, B. Korte Ed., Amsterdam 1982.

  23. H.König and M.Neumann, Mathematische Wirtschaftstheorie-mit einer Einführung in die konvexe Analysis. Mathematical Systems in Econom.100, A. Hain 1986.

  24. A. Kolmogoroff, Sur la notion de la moyenne. Atti. Regio Accad. Lincei12, 388–391 (1930).

    Google Scholar 

  25. V. Komornik, Minimax theorems for upper semicontinuous functions. Acta Math. Acad. Sci. Hung.40, 159–163 (1982).

    Google Scholar 

  26. D. H. Lehmer, On the compounding of certain means. J. Math. Anal. Appl.36, 183–200 (1971).

    Google Scholar 

  27. B.-L. Lin andX.-Ch. Quan, A symmetric minimax theorem without linear structure. Arch. Math.52, 367–370 (1989).

    Google Scholar 

  28. S. Matsumara, Über die Axiomatik von Mittelbildungen. Tôhoku Math. J. Sendai36, 260–262 (1933).

    Google Scholar 

  29. I. Nakahara, Axioms for the weighted means. Tôhoku Math. J. Sendai41, 424–434 (1936).

    Google Scholar 

  30. T. Parthasarathy, A note on a minimax theorem of T. T. Tie. Sankhyā27, Series A, 407–408 (1965).

    Google Scholar 

  31. T. Parthasarathy, On a general minimax theorem. Math. Student34, 195–197 (1966).

    Google Scholar 

  32. G. M. Phillips, Archimedes the numerical analyst. Amer. Math. Monthly88, 165–169 (1981).

    Google Scholar 

  33. R. Schimmack, Der Satz vom arithmetischen Mittel in axiomatischer Begründung. Math. Ann.68, 125–132 (1910).

    Google Scholar 

  34. S. Simons, An upward-downward minimax theorem. Arch. Math.55, 275–279 (1990).

    Google Scholar 

  35. S.Simons, On Terkelsen's minimax theorem. Bull. Inst. Math. Acad. Sinica, to appear.

  36. L. L. Stachó, Minimax theorems beyond topological vector spaces. Acta Sci. Math.42, 157–164 (1980).

    Google Scholar 

  37. F. Terkelsen, Some minimax theorems. Math. Scand.31, 405–413 (1972).

    Google Scholar 

  38. T. Tjoe-Tie, Minimax theorems on conditionally compact sets. Ann. Math. Stat.34, 1536–1540 (1963).

    Google Scholar 

  39. G. H. Toader, Generalized double sequences. L'Analyse Numérique et la Théorie de l'Approximation16, 81–85 (1987).

    Google Scholar 

  40. H. Tuy, On a general minimax theorem. Soviet. Math. Dokl.15, 1689–1693 (1974).

    Google Scholar 

  41. H. Tuy, On the general minimax theorem. Colloq. Math.33, 145–158 (1975).

    Google Scholar 

  42. Wu. Wen-Tsün, A remark on the fundamental theorem in the theory of games. Sci. Rec. New Ser.3, 229–233 (1959).

    Google Scholar 

Download references

Author information

Author notes

  1. Jürgen Kindler

    Present address: Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-6100, Darmstadt

Authors and Affiliations

    Authors
    1. Jürgen Kindler
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Kindler, J. On a minimax theorem of Terkelsen's. Arch. Math 55, 573–583 (1990). https://doi.org/10.1007/BF01191693

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01191693

    Keywords

    Search

    Navigation