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A generalization of a minimax theorem of Fan via a theorem of the alternative

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Abstract

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.

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References

  1. Fan, K.,Minimax Theorems, Proceedings of the National Academy of Sciences, USA, Vol. 39, pp. 42–47, 1953.

    Google Scholar 

  2. Van Neumann, J.,Zur Theorie der Gesellschaftsspiele, Mathematische Annalen, Vol. 100, pp. 295–320, 1928.

    Google Scholar 

  3. Browder, F.,The Fixed-Point Theory of Multivalued Mappings in Topological Vector Spaces, Mathematische Annalen, Vol. 177, pp. 177–283, 1968.

    Google Scholar 

  4. Parthasarathy, T., andRaghavan, T. E.,Some Topics in Two-Persons Games, Elsevier, New York, New York, 1971.

    Google Scholar 

  5. Balakrishnan, A. V.,Applied Functional Analysis, New York, New York, 1976.

  6. Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. Craven, B. D.,Mathematical Programming and Control Theory, Chapman and Hall, London, England, 1978.

    Google Scholar 

  10. Aubin, J. P.,Mathematical Methods of Game and Economic Theory, North-Holland, Amsterdam, Holland, 1979.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia

    V. Jeyakumar Ph.D. (Student)

Authors
  1. V. Jeyakumar Ph.D.
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Additional information

Communicated by G. Leitmann

The author is indebted to Dr. B. D. Craven for his helpful comments and suggestions toward a clear presentation of this paper.

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Jeyakumar, V. A generalization of a minimax theorem of Fan via a theorem of the alternative. J Optim Theory Appl 48, 525–533 (1986). https://doi.org/10.1007/BF00940575

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  • DOI: https://doi.org/10.1007/BF00940575

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