Mixed quasi-variational inequalities involving error bounds

In this paper, we define some new notions of gap functions for set-valued mixed quasi-variational inequalities under suitable conditions. Further, we obtain local/global bounds for the solution of set-valued mixed quasi-variational inequality problems in terms of the residual gap function, the regularized gap function, and the D-gap function. The results obtained in this paper are generalization and refinement of previously known results for some class of variational inequality problems.