ON THE VECTOR MIXED QUASI-VARIATIONAL INEQUALITY PROBLEMS

Abstract

In this paper, we introduce and consider a new class of vector mixed quasi variational inequality and vector complementarity problem in a topological vector space. We show that under certain conditions the solution set of the vector mixed quasi complementarity problem equals to the solution set of the vector mixed quasi variational inequalities. Using the Ky Fan s lemma, we study the existence of a solution of the vector mixed quasi variational inequalities and vector mixed quasi complementarity problems. Moreover we discuss on some of our assumptions. Our results extend those of Farajzadeh et al [Mixed quasi complementarity problems in topological vector spaces, J. Global. Optim.,45 (2009) 229 235] to the vector case.