摘要
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y) = u(x) + β(x)v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y) = u(x) + β(x)v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.
基金
Supported by the National Natural Science Foundation of China(No.11171362,11571055)