Abstract: In this paper, we introduce and study a class of generalized mixed variational inequalities, app lying two concep ts ofη2subdifferential andη2p roximalmapp ings of p roper functionals, we discuss existence of solutions for generalized mixed variational inequalities. Combining sp littingmethod and self2adap tive iterative method,we sug2 gest and analyze a exp licit iterative method for solving generalized mixed variational inequalities. The new iterative method converge sunder certain mild conditions.