An iterative method for generalized nonlinear set-valued mixed quasi-variational inequalities with HH-monotone mappings

Generalized nonlinear set-valued mixed quasi-variational inequalities with maximal monotone mappings have been studied in the literature. Since the maximal monotone operators are known as special cases of the HH-monotone operators, we generalize the study for these inequality problems with HH-monotone mappings in this paper. Precisely, we establish the existence of solutions for the generalized nonlinear set-valued mixed quasi-variational inequality problem with HH-monotone mappings. An iterative method for finding their approximate solutions are proposed. Furthermore, a new convergence criteria for this iterative method is imposed.