Journal of Inequalities and Applications 
Volume 5 (2000), Issue 4, Pages 397-405
doi:10.1155/S1025583400000217

Saddle point theorems on generalized convex spaces

In-sook Kim1 and Sehie Park2

 1Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
2Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Received 23 July 1999

Abstract

A sharpened extension of Komiya’s saddle point theorem is obtained for generalized convex spaces. Moreover, we show that convexity of the involved sets in his theorem can be replaced by acyclicity, and continuity of the involved functions by lower and upper semicontinuity.