Evolution of the Minimax Inequality of Ky Fan

الملخص EN

There are quite a few generalizations or applications of the 1984 minimax inequality of Ky Fan compared with his original 1972 minimax inequality.

In a certain sense, the relationship between the 1984 inequality and several hundreds of known generalizations of the original 1972 inequality has not been recognized for a long period.

Hence, it would be necessary to seek such relationship.

In this paper, we give several generalizations of the 1984 inequality and some known applications in order to clarify the close relationship among them.

Some new types of minimax inequalities are added.