Class 𝔄-KKM(X,Y,Z), General KKM Type Theorems, and Their Applications in Topological Vector Space

Abstract

The class 𝔄-$KKM(X,Y,Z)$ and generalized $KKM$ mapping are introduced, and some generalized $KKM$ theorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.