Mixed quasi complementarity problems in topological vector spaces

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