Existence and algorithm for solving some generalized mixed variational inequalities

In this paper, by applying the auxiliary variational principle technique, an existence theorem of solutions for a new class of generalized mixed variational inequalities is proved in Hilbert spaces. A novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed. The convergence criteria and error estimates are also given. These results of existence, algorithm, and convergence are new and generalize some corresponding results involving single-valued mappings in recent literatures.