Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity Academic Article uri icon


  • This paper generalizes the Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem of Ky Fan ("Game Theory and Related Topics," pp. 151-156, North-Holland, Amsterdam, 1979; and Math. Ann. 266, 1984, 519-537) and the Ky Fan minimax inequality by introducing a class of the generalized closedness and continuity conditions, which are called the transfer closedness and transfer continuities. We then apply these results to prove the existence of maximal elements of binary relations under very weak assumptions. We also prove the existence of price equilibrium and the complementarity problem without the continuity assumptions. Thus our results generalize many of the existence theorems in the literature. 1992.

published proceedings

  • Journal of Mathematical Analysis and Applications

author list (cited authors)

  • Tian, G.

citation count

  • 116

complete list of authors

  • Tian, Guoqiang

publication date

  • January 1992