On the convergence analysis of the iterative method with errors for general mixed quasivariational. inequalities in Hilbert spaces

The purpose of this paper is to investigate the iterative methods for a class of general mixed quasivariational inequalities in a Hilbert space. Utilizing the alternative equivalent formulation between general mixed quasivariational inequalities and implicit fixed-point problems, we suggest and analyze a new modified self-adaptive resolvent method with errors for solving this class of general mixed quasivariational inequalities in conjunction with a technique updating the solution. Moreover, we give the convergence analysis of this method in a Hilbert space. Since this class of general mixed quasivariational. inequalities includes a number of known classes of variational inequalities as special cases, our results are more general than some earlier and recent ones in the literature.