Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 397-405

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

Copyright © 2000 In-sook Kim and Sehie Park. 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.


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.