Remarks on saddle points of vector-valued functions

Authors : Insook KİM

Pages : 72-77

Doi:10.53006/rna.1086597

View : 20 | Download : 14

Publication Date : 2022-03-31

Article Type : Research Paper

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