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Proceedings of the American Mathematical Society

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Systems of inequalities involving convex functions

Authors: Ky Fan, Irving Glicksberg and A. J. Hoffman
Journal: Proc. Amer. Math. Soc. 8 (1957), 617-622
MSC: Primary 90.0X
MathSciNet review: 0087574
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  • [1] N. Bourbaki, Espaces vectoriels topologiques, Chapters I, II, Paris, 1953.
  • [2] Walter B. Carver, Systems of linear inequalities, Ann. of Math. (2) 23 (1922), no. 3, 212–220. MR 1502612, 10.2307/1967919
  • [3] Ky Fan, On systems of linear inequalities, Linear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, pp. 99–156. MR 0087901
  • [4] J. Farkas, Theorie der einfachen Ungleichungen, J. Reine Angew. Math. vol. 124 (1902) pp. 1-27.
  • [5] David Gale, Harold W. Kuhn, and Albert W. Tucker, Linear programming and the theory of games, Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons, Inc., New York, N. Y.,; Chapman & Hall, Ltd., London, 1951, pp. 317–329. MR 0046018
  • [6] John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944. MR 0011937
  • [7] H. Weyl, Elementare Theorie der konvexen Polyeder, Comment. Math. Helv. 7 (1934), no. 1, 290–306 (German). MR 1509514, 10.1007/BF01292722

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Article copyright: © Copyright 1957 American Mathematical Society