Iterative Methods for General Mixed Quasi Variational Inequalities

It is well known that mixed quasi variational inequalities are equivalent to implicit fixed-point problems. We use this alternative equivalent formulation to suggest and analyze a new self-adaptive resolvent method for solving mixed quasi variational inequalities in conjunction with a technique updating the solution. We show that the convergence of this method requires pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasi variational inequalities include various classes of variational inequalities as special cases, our results continue to hold for these problems