Auxiliary Principle and Iterative Algorithm for a System of Generalized Nonlinear Mixed Quasi-variational-like Inequalities

In this paper, the auxiliary principle technique is extended to study a system of generalized nonlinear mixed quasi-variational-like inequalities in Hilbert spaces. First, we establish the existence of solutions of the corresponding system of auxiliary generalized nonlinear mixed qusi-variational-like inequalities. Then based on the existence result, we construct a new iterative algorithm. Finally, both the existence of solutions of the original problem and the convergence of iterative sequences generated by the algorithm are proved. Our results improve and extend some known results.