Minimax Problems for Set-Valued Mappings
Y. Zhang, Sichen Li, Shengkun Zhu · Numerical Functional Analysis and Optimization · 2012
In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.