The purpose of this paper is to introduce a class of new random completely
generalized set-valued implicit quasi-variational inequalities, to construc
t new random iterative algorithms, and to give some existence theorems of r
andom solutions for this class of random completely generalized set-valued
implicit quasi-variational inequalities. We also prove the convergence of r
andom iterative sequences generated by the algorithms. Our results extend a
nd improve the earlier and recent results.