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 quasicomplementarity 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. 2000 Mathematics subject classification: 49J40, 90C33.