Abstract
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 H -monotone operators, we generalize the study for these inequality problems with H -monotone mappings in this paper. Precisely, we establish the existence of solutions for the generalized nonlinear set-valued mixed quasi-variational inequality problem with H -monotone mappings. An iterative method for finding their approximate solutions are proposed. Furthermore, a new convergence criteria for this iterative method is imposed.
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