Skip to main content
Log in

Some Intersection Theorems and Minimax Inequalities

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper proves some intersection theorems. The proofs are new in the sense that they do not require the finite intersection property. As an application, some of the Fan minimax inequalities are proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. FAN, K., Minimax Inequalities and Applications, Inequalities, Edited by X. X. Shisha, Academic Press, New York, New York, Vol. 3, pp. 103–113, 1972.

    Google Scholar 

  2. KAKUTANI, S., A Generalization of Brouwer's Fixed-Point Theorem, Duke Mathematical Journal, Vol. 8, pp. 457–459, 1941.

    Google Scholar 

  3. CUBIOTTI, P., Some Remarks on Fixed Points of Lower Semicontinuous Multifunctions, Journal of Mathematical Analysis and Applications, Vol. 174, pp. 407–412, 1993.

    Google Scholar 

  4. MICHAEL, E., Continuous Selections, I, Annals of Mathematics, Vol. 63, pp. 361–382, 1956.

    Google Scholar 

  5. AUBIN, J., and CELLINA, A., Differential Inclusions: Set-Valued Maps and Viability Theory, Springer Verlag, New York, New York, 1984.

    Google Scholar 

  6. SCHAUDER, J., Der Fixpunktsatz in Funktionalraumen, Studia Mathematica, Vol. 2, pp. 171–180, 1930.

    Google Scholar 

  7. BARDARO, C., and CEPPITELLI, R., Some Further Generalizations of the Knaster-Kuratowski-Mazurkiewicz Theorem and Minimax Inequalities, Journal of Mathematical Analysis and Applications, Vol. 132, pp. 484–490, 1988.

    Google Scholar 

  8. PARK, S., Generalizations of Ky Fan's Matching Theorem and Their Applications, Journal of Mathematical Analysis and Applications, Vol. 141, pp. 164–176, 1989.

    Google Scholar 

  9. CHANG, S. S., and ZHANG, Y., Generalized KKM Theorem and Variational Inequalities, Journal of Mathematical Analysis and Applications, Vol. 159, pp. 208–223, 1991.

    Google Scholar 

  10. CHANG, S. S., and MA, Y. H., Generalized KKM Theorem on H-Space with Applications, Journal of Mathematical Analysis and Applications, Vol. 163, pp. 406–421, 1992.

    Google Scholar 

  11. BORDER, K. C., Fixed-Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, England, 1985.

    Google Scholar 

  12. YUAN, X. Z., Contribution to Nonlinear Analysis, PhD Thesis, Dalhousie University, Halifax, Nova Scotia, Canada, 1993.

  13. TIAN, G. Q., Generalization of the KKM Theorem and the Ky Fan Minimax Inequality with Applications to Maximal Elements, Price Equilibrium, and Complementarity, Journal of Mathematical Analysis and Applications, Vol. 170, pp. 457–471, 1992.

    Google Scholar 

  14. FAN, K., A Generalization of Tychonoff's Fixed-Point Theorem, Mathematische Annalen, Vol. 266, pp. 519–537, 1961.

    Google Scholar 

  15. HORVATH, C., Some Results on Multivalued Mappings and Inequalities without Convexity, Nonlinear and Convex Analysis, Lecture Notes in Pure and Applied Mathematics, Dekker, New York, New York, Vol. 107, 1987.

    Google Scholar 

  16. KNASTER, B., KURATOWSKI, K., and MAZURKIEWICZ, S., Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe, Fundamenta Mathematicae, Vol. 14, pp. 132–137, 1929.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, X. Some Intersection Theorems and Minimax Inequalities. Journal of Optimization Theory and Applications 94, 195–207 (1997). https://doi.org/10.1023/A:1022620021924

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022620021924

Navigation