Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In this note we present we present a new elementary approach in the theory of minimax inequalities. The proof of the main result (called the geometric principle) uses only some simple properties of convex functions. The geometric principle (which is equivalent to the well-known lemma of Klee [13]) is shown to have numerous applications in different areas of mathematics.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
1-18
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-08-09
Twórcy
autor
- Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada, H3C 3J7
autor
- Département de Mathématiques, Université Blaise Pascal, 63177 Aubière Cedex, France
Bibliografia
- [1] H. Asakawa, Maximal monotone operators associated with saddle functions, TRU Math. 22 (2) (1986), 47-71.
- [2] C. Berge, Espaces topologiques, Fonctions multivoques, Dunod, Paris 1959.
- [3] H. F. Bohnenblust, S. Karlin and L. Shapley, Games with continuous pay-off, in: Ann. of Math. Stud. 24 (1950), 181-192
- [4] H. Debrunner und P. Flor, Ein Erweiterungssatz für monotone Mengen, Arch. Math. (Basel) 15 (1964), 445-447.
- [5] J. Dugundji and A. Granas, Fixed Point Theory, Vol. I, Monografie Mat. 61, Polish Scientific Publishers, Warszawa 1982.
- [6] K. Fan, Minimax theorems, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42-47.
- [7] K. Fan, Existence theorems and extreme solutions for inequalities concerning convex functions or linear transformations, Math. Z. 68 (1957), 205-216.
- [8] K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305-310.
- [9] K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234-240.
- [10] K. Fan, A minimax inequality and applications, in: Inequalities III, O. Shisha (ed.), Academic Press, New York 1972, 103-113.
- [11] K. Fan, I. Glicksberg and A. J. Hoffman, Systems of inequalities involving convex functions, Proc. Amer. Math. Soc. 8 (1957), 617-622.
- [12] B. Halpern and G. Bergman, A fixed point theorem for inward and outward maps, Trans. Amer. Math. Soc. 130 (1968), 353-358.
- [13] V. L. Klee, On certain intersection properties of convex sets, Canad. J. Math. 3 (1951), 272-275.
- [14] B. Knaster, C. Kuratowski und S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math. 14 (1929), 132-137.
- [15] H. Kneser, Sur un théorème fondamental de la théorie des jeux, C. R. Acad. Sci. Paris 234 (1952), 2418-2420.
- [16] H. König, Über das von Neumannsche minimax theorem, Arch. Math. (Basel) 19 (1968), 482-487.
- [17] M. Lassonde, Multi-applications KKM en analyse non linéaire, Thèse de Doctorat, Université de Montréal, 1978.
- [18] M. Neumann, Bemerkungen zum von Neumannschen Minimaxtheorem, Arch. Math. (Basel) 29 (1977), 96-105.
- [19] H. Nikaidô, On von Neumann's minimax theorem, Pacific J. Math. 4 (1954), 65-72.
- [20] M. Sion, On general minimax theorems, ibid. 8 (1958), 171-176.
- [21] E. Sperner, Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes, Abh. Math. Sem. Univ. Hamburg 6 (1928), 265-272.
- [22] F. A. Valentine, Convex Sets, McGraw-Hill, New York 1964.
Typ dokumentu
Bibliografia
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