Minimax Theorems for Set-Valued Mappings under Cone-Convexities

Minimax Theorems for Set-Valued Mappings under Cone-Convexities

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The aim of this paper is to study the minimax theorems for set-valued mappings with or without linear structure.We define several kinds of cone-convexities for set-valued mappings, Boardshorts give some examples of such set-valued mappings, and Tall Pier study the relationships among these cone-convexities.By using our minimax theorems, we derive some existence results for saddle points of set-valued mappings.Some examples to illustrate our results are also given.