Remarks on saddle points of vector-valued functions

Abstract

Using a coincidence theorem for multimaps, we prove the existence of a saddle point for vector-valued functions in topological vector spaces by means of scalarized maps. Moreover, we discuss minimax theorems as a consequence of the saddle point theorem for real-valued functions.

Keywords

• saddle point
• minimax theorem
• coincidence theorem
• upper (lower) semicontinuity
• multimap

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