A generalization of a minimax theorem of Fan via a theorem of the alternative
Tóm tắt
The paper contains a version of a minimax theorem with weakened convexity, extending a minimax theorem of Fan. The main result is obtained with the use of a generalized Gordan theorem, which is proved using a separation theorem. An example is also discussed.
Tài liệu tham khảo
Fan, K.,Minimax Theorems, Proceedings of the National Academy of Sciences, USA, Vol. 39, pp. 42–47, 1953.
Van Neumann, J.,Zur Theorie der Gesellschaftsspiele, Mathematische Annalen, Vol. 100, pp. 295–320, 1928.
Browder, F.,The Fixed-Point Theory of Multivalued Mappings in Topological Vector Spaces, Mathematische Annalen, Vol. 177, pp. 177–283, 1968.
Parthasarathy, T., andRaghavan, T. E.,Some Topics in Two-Persons Games, Elsevier, New York, New York, 1971.
Balakrishnan, A. V.,Applied Functional Analysis, New York, New York, 1976.
Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.
Fan, K., Glicksberg, I., andHoffman, A. J.,Systems of Inequalities Involving Convex Functions, Proceedings of the American Mathematical Society, Vol. 8, pp. 617–622, 1957.
Eisenberg, E.,On Cone Functions, Recent Advances in Mathematical Programming, Edited by P. Wolfe and R. L. Graves, McGraw-Hill Book Company, New York, New York, pp. 27–33, 1963.
Craven, B. D.,Mathematical Programming and Control Theory, Chapman and Hall, London, England, 1978.
Aubin, J. P.,Mathematical Methods of Game and Economic Theory, North-Holland, Amsterdam, Holland, 1979.