Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities

Abstract

In this paper, by applying the auxiliary variational principle technique, some existence theorems of solutions for a class of generalized mixed implicit quasi-variational inequalities are proved in Hilbert spaces. A novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed. The convergence criteria are also given. As special cases of these results, the open problem put forward by Noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi-complementarity problems are also obtained. Our results are new and generalize a number of known results of mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementary problems involving single-valued and set-valued mappings in recent literatures.