Remarks on saddle points of vector-valued functions

Year 2022, Volume: 5 Issue: 1, 72 - 77, 31.03.2022

In-sook Kim

https://doi.org/10.53006/rna.1086597

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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