Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 4, Pages 493-505
doi:10.1155/S1048953398000409
A G-KKM type theorem and its applications to minimax inequalities on G-convex spaces
Dalhousie University, Department of Mathematics, Statistics and Computing Science, Nova Scotia, Halifax B3H 3J5, Canada
Received 1 September 1996; Revised 1 January 1998
Copyright © 1998 Mohammad S. R. Chowdhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A G-KKM type theorem is obtained on G-convex spaces. As application,
a generalization of Ky Fan's minimax inequality to non-compact sets on
G-convex spaces is first obtained. As special cases of this minimax
inequality, some new minimax inequalites are obtained. Four fixed point
theorems and four equivalent formulations of the second minimax
inequality are also obtained.