The 2-KKM property and its applications in hyperconvex metric spaces

Abstract

In this work, we first define the generalized 2- KKM mapping and the family 2- KKM ( X , Y ) on a metric space, and then we apply these properties to get a 2- KKM theorem and a fixed point theorem without a compactness assumption. Next, by using these 2- KKM theorems, we get some variational inequality theorems and minimax inequality theorems.