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

Mohammad S. R. Chowdhury

 Dalhousie University, Department of Mathematics, Statistics and Computing Science, Nova Scotia, Halifax B3H 3J5, Canada
Received 1 September 1996; Revised 1 January 1998

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.