Saddle point theorems on generalized convex spaces

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.

Keywords

• Generalized convex space
• Saddle point
• Lower or upper semicontinuous function
• Acyclic map
• Coincidence theorem
• Minimax theorem