Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces

In the paper, the notions of generalized loose (weak) saddle points for set-valued mappings are introduced. By applying the fixed point theorem and the scalarization method, some new existence theorems for generalized loose (weak) saddle points are established in locally GG-convex space. As applications, some vector minimax theorems are given also.