Remarks on saddle points of vector-valued functions
Authors : In-sook Kim
Pages : 72-77
Doi:10.53006/rna.1086597
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Publication Date : 2022-03-31
Article Type : Research
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