Minimax Theory For Set-valued Mappings

In this thesis, we study two problems: minimax inequalities for set-valued mappings and minimax theorem for two scalar set-valued mappings. It is organized as follows:Firstly, we use a nonlinear scalarization function and its strict monotonicity property to verify minimax inequalities for set-valued mappings in a Hausdorff topological vector space. two examples are given to illustrate our results.Secondly, we generalize the generalized minimax theorem for a scalar set-valued mapping of Li [39]to the case of two scalar set-valued mappings, in which concavity and convexity of the mappings is weaker.