In this paper, we suggest and consider a class of new three-step
approximation schemes for generalized general set-valued mixed quasi variational
inequalities. We also consider and analyze a new class of extragradient-type
methods for solving generalized set-valued variational inequalities. The
proposed methods include several new and known methods as special cases.
Our results present a significant improvement of previously known methods
for solving variational inequalities and related optimization problems.