Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces

For vector-valued functions, cone saddle points are defined, and some existence theorems for them are established in infinite-dimensional spaces. Most of our results rely on Condition 2.1, which has been given by Sterna-Karwat. In particular, it shows that the scalarization of vector-valued functions plays an important role for the condition. Some interesting examples in infinite-dimensional spaces are presented. Moreover, necessary conditions for the existence of cone saddle points are investigated.The author would like to thank the referees for their valuable suggestions on the original draft.