THE MINIMAX PROBLEM OF TWO VECTOR-VALUED FUNCTIONS

Abstract

In this paper, we study the minimax problem in a partial ordered Hausdorff topological vector space. We obtain a vector form Ky Fan minimax inequality theorem which involves two vector-valued functions. The proof of this theorem don’t use separation theorems and nonlinear scalarization functions. Forthermore, we also use the fixed point theorem of set-valued mappings by Browder [1] to prove some results of minimax problem of two vector-valued functions, and the minimax theorem in [16] is extended to vector form.