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Coincidence and some systems of inequalities
Hukukane NIKAIDÔ
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Hukukane NIKAIDÔ
The Institute of Social and Economic Research, Osaka University
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1959 Volume 11 Issue 4 Pages 354-373
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- Published: 1959 Received: April 27, 1959 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: August 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Hukukane NIKAIDO1)
Right : Hukukane NIKAIDÔ1)
Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K.J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
2) E.G. Begle, A fixed point theorem, Ann. Math., 51 (1950), 544-550.
3) E.G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. Math., 51 (1950), 534-543.
4) N. Bourbaki, Éléments de mathématiques, libre V, Espaces vectoriels topologiques, 1953.
5) G. Debreu, Market equilibrium, Proc. Nat. Acad. Sci., U.S.A., 42 (1956), 876-878.
6) S. Eilenberg and D. Montgomery, Fixed point-theorems for multivalued transformations, Amer. J. Math., 68 (1946), 214-222.
7) K. Fan, Minimax theorems, Proc. Nat. Acad. Sci., U.S.A., 39 (1953), 42-47.
8) K. Fan, On systems of linear inequalities, in Linear inequalities and related systems', (1956), Ann. Math. Studies, No. 38, 99-156.
9) W. Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann., 101 (1929), 238-252.
10) D. Gale, The law of supply and demand, Math. Scad., 3 (1955), 155-169.
11) R.A. Hirschfeld, On a minimax theorem of K. Fan, Koninkl. Nederl. Akad. Wet., Proc. Series A, 61 (1958), and Indag. Math., 20 (1958), 470-474.
12) S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457-459.
13) B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math., 14 (1926), 132-138.
14) H. Kneser, Sur un théorème fondamental de la théorie des jeux, C.R. Acad. Sci. Paris, 234 (1952), 2418-2420.
15) H.W. Kuhn and A.W. Tucker, eds., Contributions to the theory of games, 1 (1950), Ann. Math. Studies, No. 24.
16) S. Lefschetz, On the fixed point formula, Ann. Math., 38 (1937), 819-822.
17) S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloq. Publ., 27, 1942.
18) L.W. McKenzie, On equilibrium in Graham's model of world trade and other competitive systems, Econometrica, 22 (1954), 147-161.
19) J.F. Nash, Equilibrium points in n-person games, Proc. Nat. Acad. Sci., U.S.A., 36 (1950), 48-49.
20) J.F. Nash, Non-cooperative games, Ann. Math., 54 (1951), 286-295.
21) J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann., 100 (1928), 295-320.
22) J. von Neumann, Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, Ergeb. Math, Kolloq., 8 (1937), 73-83.
23) J. von Neumann, Theory of games and economic behavior, with O. Morgenstern, Princeton Univ. Press, 1944.
24) H. Nikaido, On von Neumann's minimax theorem, Pacif. J. Math., 4 (1954), 65-72.
25) H. Nikaido, Note on noncooperative convex games, with K. Isoda, Pacif. J. Math., 5 (1955), Supplement I, 807-815.
26) H. Nikaido, On the classical multilateral exchange problem, Metroeconomica, 8 (1956), 135-145; A supplementary note to [26], Metroeconomica, 9 (1957), 209-210.
27) H. Nikaido, On a minimax theorem and its applications to functional analysis, J. Math. Soc. Japan, 5 (1953), 86-94.
28) H. Nikaido, On the existence of competitive equilibrium for infinitely many commodities, Tech. Report, 34 (1956), Dept, of Econ., Stanford Univ.
29) H. Nikaido, Existence of equilibrium based on the Walras law, ISER Discussion Paper No. 2 (1957), Inst. Soc. and Econ. Research, Osaka University.
30) M. Sion, On general minimax theorems, Pacif. J. Math., 8 (1958), 171-176.
31) L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann., 97 (1927), 454-472.
32) L. Walras, Éléments d'économie politique pure, Lausanne, Paris, 1900.
Right : 1) K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica, 22 (1954), 265-290.
2) E. G. Begle, A fixed point theorem, Ann. Math., 51 (1950), 544-550.
3) E. G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. Math., 51 (1950), 534-543.
4) N. Bourbaki, Éléments de mathématiques, libre V, Espaces vectoriels topologiques, 1953.
5) G. Debreu, Market equilibrium, Proc. Nat. Acad. Sci., U. S. A., 42 (1956), 876-878.
6) S. Eilenberg and D. Montgomery, Fixed point-theorems for multivalued transformations, Amer. J. Math., 68 (1946), 214-222.
7) K. Fan, Minimax theorems, Proc. Nat. Acad. Sci., U. S. A., 39 (1953), 42-47.
8) K. Fan, On systems of linear inequalities, in ‘Linear inequalities and related systems’, (1956), Ann. Math. Studies, No. 38, 99-156.
9) W. Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann., 101 (1929), 238-252.
10) D. Gale, The law of supply and demand, Math. Scad., 3 (1955), 155-169.
11) R. A. Hirschfeld, On a minimax theorem of K. Fan, Koninkl. Nederl. Akad. Wet., Proc. Series A, 61 (1958), and Indag. Math., 20 (1958), 470-474.
12) S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457-459.
13) B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe, Fund. Math., 14 (1926), 132-138.
14) H. Kneser, Sur un théorème fondamental de la théorie des jeux, C. R. Acad. Sci. Paris, 234 (1952), 2418-2420.
15) H. W. Kuhn and A.W. Tucker, eds., Contributions to the theory of games, 1 (1950), Ann. Math. Studies, No. 24.
16) S. Lefschetz, On the fixed point formula, Ann. Math., 38 (1937), 819-822.
17) S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloq. Publ., 27, 1942.
18) L.W. McKenzie, On equilibrium in Graham's model of world trade and other competitive systems, Econometrica, 22 (1954), 147-161.
19) J. F. Nash, Equilibrium points in n-person games, Proc. Nat. Acad. Sci., U. S. A., 36 (1950), 48-49.
20) J. F. Nash, Non-cooperative games, Ann. Math., 54 (1951), 286-295.
21) J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann., 100 (1928), 295-320.
22) J. von Neumann, Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, Ergeb. Math, Kolloq., 8 (1937), 73-83.
23) J. von Neumann, Theory of games and economic behavior, with O. Morgenstern, Princeton Univ. Press, 1944.
24) H. Nikaidô, On von Neumann's minimax theorem, Pacif. J. Math., 4 (1954), 65-72.
25) H. Nikaidô, Note on noncooperative convex games, with K. Isoda, Pacif. J. Math., 5 (1955), Supplement I, 807-815.
26) H. Nikaidô, On the classical multilateral exchange problem, Metroeconomica, 8 (1956), 135-145; A supplementary note to [26], Metroeconomica, 9 (1957), 209-210.
27) H. Nikaidô, On a minimax theorem and its applications to functional analysis, J. Math. Soc. Japan, 5 (1953), 86-94.
28) H. Nikaidô, On the existence of competitive equilibrium for infinitely many commodities, Tech. Report, 34 (1956), Dept, of Econ., Stanford Univ.
29) H. Nikaidô, Existence of equilibrium based on the Walras law, ISER Discussion Paper No. 2 (1957), Inst. Soc. and Econ. Research, Osaka University.
30) M. Sion, On general minimax theorems, Pacif. J. Math., 8 (1958), 171-176.
31) L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann., 97 (1927), 454-472.
32) L. Walras, Éléments d'économie politique pure, Lausanne, Paris, 1900.
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