Abstract
A generalization of Simons's metaminimax theorem to a metaminimax theorem involving two functions is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cao-Zong Cheng and You-Hao Lin, A generalization of minimax theorems of fixed-point type, Acta Math. Sinica, 34 (1991), 502–507.
Cao-Zong Cheng and Bor-Luh Lin, A two functions, noncompact topological minimax theorem, Acta Math. Hungar., 73 (1996), 65–69.
Ky Fan, Minimax theorems, Proc. Nat. Acad. Sci. U.S.A., 39 (1953), 42–47.
M. A. Geraghty and Bor-Luh Lin, On a minimax theorem of Terkelsen, Bull. Inst. Math. Acad. Sinica, 11 (1983), 343–347.
M. A. Geraghty and Bor-Luh Lin, Topological minimax theorem, Proc. Amer. Math. Soc., 91 (1984), 377–380.
M. A. Geraghty and Bor-Luh Lin, Minimax theorems without linear structure, Linear and Multilinear Algebra, 17 (1985), 171–180.
M. A. Geraghty and Bor-Luh Lin, Minimax theorems without convexity, Contemporary Math., 52 (1986), 102–108.
Chung-Wei Ha, Minimax and fixed point theorems, Math. Ann., 248 (1983), 73–77.
A. Irle, A general minimax theorem, Zeitschrift für Operations Research, 29 (1985)
J. Kindler and R. Trost, Minimax theorems for interval spaces, Acta Math. Hungar., 54 (1989), 39–49.
J. Kindler, On a minimax theorem of Terkelsen's, Arch. Math., 55 (1990), 35–39.
V. Komornik, Minimax theorems for upper semi-continuous functions, Acta Math. Acad. Sci. Hungar., 40 (1982), 159–163.
H. König, Über das von Neumannsche Minimax-Theorem, Arch. Math., 19 (1968), 482–487.
Bor-Luh Lin and X. C. Quan, A symmetric minimax theorem without linear structure, Arch. Math., 52 (1989), 367–370.
M. Neumann, Bemerkungen zum von Neumannschen Minimax theorem, Arch. Math., 29 (1977), 96–105.
S. Simons, An upward-downward minimax theorem, Arch. Math., 55 (1990), 275–279.
S. Simons, On Terkelsen minimax theorems, Bull. Inst. Math. Acad. Sinica, 18 (1990), 35–39.
S. Simons, A flexible minimax theorem, Acta Math. Hungar., 63 (1994), 119–132.
S. Simons, Addendum to “A flexible minimax theorem”, Acta Math. Hungar., 69 (1995), 359–360.
S. Simons, Minimax theorems and their proofs, Minimax and Applications (ed. by D. Z. Du and P. M. Pardolos), Kluwer Academic Publishers (1995), 1–23.
M. Sion, On general minimax theorem, Pacific J. Math., 8 (1958), 171–176.
L. L. Stachó, Minimax theorems beyond topological vector spaces, Acta Sci. Math. (Szeged), 42 (1980), 157–164.
F. Terkelsen, Some minimax theorems, Math. Scand., 31 (1972), 405–413.
H. Tuy, On a general minimax theorem, Soviet Math. Dokl., 15 (1974), 1689–1693.
H. Tuy, On the general minimax theorem, Colloquium Math., 33 (1975), 145–158.
W. T. Wu, A remark on the fundamental theorem in the theory of games, Sci. Record New Ser., 3 (1959), 229–233.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lin, BL., Yu, FS. A Two Function Metaminimax Theorem. Acta Mathematica Hungarica 83, 115–123 (1999). https://doi.org/10.1023/A:1006671721304
Issue Date:
DOI: https://doi.org/10.1023/A:1006671721304