Separation and von Neumann intersection theorems

Chang, Shiow Yu

doi:10.1090/S0002-9939-1991-1070512-3

Separation and von Neumann intersection theorems
HTML articles powered by AMS MathViewer

by Shiow Yu Chang

Proc. Amer. Math. Soc. 112 (1991), 1149-1152

DOI: https://doi.org/10.1090/S0002-9939-1991-1070512-3

PDF | Request permission

Abstract:

We give some separation theorems to extend the intersection theorem of von Neumann, Fan, and others, omitting hypotheses of convexity and local convexity for one of the coordinate spaces.

References

Ky. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121–126. MR 47317, DOI 10.1073/pnas.38.2.121
I. L. Glicksberg, A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170–174. MR 46638, DOI 10.1090/S0002-9939-1952-0046638-5
Chung Wei Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), no. 1, 73–77. MR 569411, DOI 10.1007/BF01349255

A generalization of Brouwer’s fixed point theorem

7

J. v. Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928), no. 1, 295–320 (German). MR 1512486, DOI 10.1007/BF01448847

Uber ein okonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes

8

Nicholas C. Yannelis and N. D. Prabhakar, Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), no. 3, 233–245. MR 743037, DOI 10.1016/0304-4068(83)90041-1