Minimax theorems with applications to convex metric spaces

Jürgen Kindler

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 2, page 179-186
  • ISSN: 0010-1354

Abstract

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A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.

How to cite

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Kindler, Jürgen. "Minimax theorems with applications to convex metric spaces." Colloquium Mathematicae 68.2 (1995): 179-186. <http://eudml.org/doc/210301>.

@article{Kindler1995,
abstract = {A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.},
author = {Kindler, Jürgen},
journal = {Colloquium Mathematicae},
keywords = {minimax theorems; minimax theorem of Ky Fan; convex metric spaces},
language = {eng},
number = {2},
pages = {179-186},
title = {Minimax theorems with applications to convex metric spaces},
url = {http://eudml.org/doc/210301},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Kindler, Jürgen
TI - Minimax theorems with applications to convex metric spaces
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 2
SP - 179
EP - 186
AB - A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.
LA - eng
KW - minimax theorems; minimax theorem of Ky Fan; convex metric spaces
UR - http://eudml.org/doc/210301
ER -

References

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  1. [1] A. A. Astaneh, On singletonness of uniquely remotal sets, Indian J. Pure Appl. Math. 17 (9) (1986), 1137-1139. Zbl0612.46018
  2. [2] R. G. Bilyeu, Metric definition of the linear structure, Proc. Amer. Math. Soc. 25 (1970), 205-206. Zbl0194.14601
  3. [3] L. M. Blumenthal and K. Menger, Studies in Geometry, Freeman, San Francisco, 1970. Zbl0204.53401
  4. [4] J. Cleary, S. A. Morris and D. Yost, Numerical geometry-numbers for shapes, Amer. Math. Monthly 93 (1986), 260-275. Zbl0598.51014
  5. [5] M. De Wilde, Doubles limites ordonnées et théorèmes de minimax, Ann. Inst. Fourier (Grenoble) 24 (1974), 181-188. Zbl0289.49019
  6. [6] K. Fan, Minimax theorems, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42-47. 
  7. [7] I. Glicksberg, Minimax theorem for upper and lower semi-continuous payoffs, The RAND Corporation Research Memorandum RM-478 (1950). 
  8. [8] O. Gross, The rendezvous value of a metric space, in: Advances in Game Theory, Ann. of Math. Stud. 52, Princeton Univ. Press, 1964, 49-53. Zbl0126.16401
  9. [9] Y. Kijima, Fixed points of nonexpansive self-maps of a compact metric space, J. Math. Anal. Appl. 123 (1987), 114-116. Zbl0618.47049
  10. [10] J. Kindler, Minimaxtheoreme und das Integraldarstellungsproblem, Manuscripta Math. 29 (1979), 277-294. Zbl0425.90089
  11. [11] J. Kindler, Minimaxtheoreme für die diskrete gemischte Erweiterung von Spielen und ein Approximationssatz, Math. Operationsforsch. Statist. Ser. Optim. 11 (1980), 473-485. Zbl0453.90104
  12. [12] J. Kindler, Minimax theorems with one-sided randomization, Acta Math. Hungar., to appear. Zbl0854.90144
  13. [13] H. König, Über das von Neumannsche Minimax-Theorem, Arch. Math. (Basel) 19 (1968), 482-487. Zbl0179.21001
  14. [14] S. A. Morris and P. Nickolas, On the average distance property of compact connected metric spaces, Arch. Math. (Basel) 40 (1983), 459-463. Zbl0528.54028
  15. [15] M. Neumann, Bemerkungen zum von Neumannschen Minimaxtheorem, ibid. 29 (1977), 96-105. 
  16. [16] J. E. L. Peck and A. L. Dulmage, Games on a compact set, Canad. J. Math. 9 (1957), 450-458. Zbl0078.32704
  17. [17] I. F. Pinelis, On minimax risk, Theory Probab. Appl. 35 (1990), 104-109. Zbl0711.62008
  18. [18] I. F. Pinelis, On minimax estimation of regression, ibid., 500-512. 
  19. [19] W. Stadje, A property of compact connected spaces, Arch. Math. (Basel) 36 (1981), 275-280. Zbl0457.54017
  20. [20] W. Takahashi, A convexity in metric space and nonexpansive mappings, I, Kōdai Math. Sem. Rep. 22 (1970), 142-149. Zbl0268.54048
  21. [21] L. Yang and J. Zhang, Average distance constants of some compact convex space, J. China Univ. Sci. Tech. 17 (1987), 17-23. Zbl0646.54035

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