On Equilibrium for Abstract Economies in GFC-Spaces

In this paper, the GFC-KKM mapping is introduced and GFC-KKM theorems are established in GFC-spaces. As applications, a fixed point theorem and maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, equilibrium existence theorems for qualitative games and abstract economies are yielded in GFC-spaces.

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.

KKM Type Theorem and Ky Fan's Inequalities in Abstract Convex Spaces

In this paper, we first prove some type theorem based on the F-KKM mapping and generalized F-KKM mapping in abstract convex space. From this, we establishsome Ky Fan's inequalities.

GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.