Generalized 2-gKKM2-gKKM property in a hyperconvex metric space and its applications

In this paper, we first define the family 2-gKKM(X,Y)2-gKKM(X,Y) in a hyperconvex metric space, and then we get a 2-gKKM2-gKKM theorem and a fixed point theorem without compactness assumption. Next, by using the 2-gKKM2-gKKM theorem, we get the matching theorems, coincidence theorems, variational inequality theorems and minimax inequality theorems.