The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

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.

A Matching Theorem in GFC-Spaces with Application to Saddle Points

In this paper, a matching theorem for weakly transfer compactly open valued mappings is established in GFC-spaces. As applications, a fixed point theorem, a minimax inequality and a saddle point theorem are obtained in GFC-spaces. Our results unify, improve and generalize some known results in recent reference.