Iterative Algorithms For Some Quasi-variational Inequalities

In this dissertation, we mainly study the iterative algorithms for a system of extended general strongly nonlinear quasi-variational inequalities and a nonconvex strongly nonlinear quasi-variational inequality. This dissertation is divided into three chapters.In chapter 1, we introduce the history of the quasi-variational inequality,the background and primary contents of this dissertation.In chapter 2, we introduce a algorithm for a new system of extended general strongly nonlinear quasi-variational inequalities in Hilbert space. First, we estab-lish the equivalence between the system of extended general strongly nonlinear quasi-variational inequalities and fixed point problems. By using these equiva-lences, we discuss the existence and uniqueness of the solution of the system of extended general strongly nonlinear quasi-variational inequalities. And then, we suggest a projection iterative algorithm with mixed errors for finding the unique solution of the system of extended general strongly nonlinear quasi-variational inequalities. Finally, we prove the convergence of the proposed iterative algorith-m.In chapter 3, we introduce a algorithm for a new nonconvex strongly nonlin-ear quasi-variational inequality in Hilbert space. First, we establish the equiva-lence between the nonconvex strongly nonlinear quasi-variational inequality, non-convex strongly nonlinear quasi-variational inclusion and fixed point problems. And then, we discuss the existence and uniqueness of the solution of the non-convex strongly nonlinear quasi-variational inequality. After that, we suggest a projection iterative algorithm with mixed errors for finding the solution of the nonconvex strongly nonlinear quasi-variational inequality. Finally, we prove the convergence of the proposed iterative algorithm.