Class𝔄-KKM(X,Y,Z), GeneralKKMType Theorems, and Their Applications in Topological Vector Space

The class𝔄-KKM(X,Y,Z)and generalizedKKMmapping are introduced, and some generalizedKKMtheorems 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.