Algorithms For General And Generalized Mixed Implicit Quasi-variational Inequalities

It is well known that the general and generalized mixed implicit quasi-variational inequalities are equivalent to the implicit resolvent equations.Recently, Deng and author[64, 65] use the alternative formulation to suggest and analyze some new algorithms for solving general and generalized mixed implicit quasi-variational inequalities. Our results improve and generalize some rencent corresponding results.The thesis is composed of three sections. First, we show the real background of the problems we study and the main works that have been studied by many authors. We also introduce some basic definition and the main results in this article. Second, we study General Mixed Implicit Quasi-variational Inequalities,and use the equivalent between the General Mixed Implicit Quasi-variational Inequalities and implicit resolvent equations to suggest and analyze some new algorithms,finally we prove the convergence of them in g-Pseudomontone operation condition. In the last section, we study generalized Mixed Implicit Quasi-variational Inequalities,and use the implicit resolvent equations technique to suggest some new algorithms of sloving generalized Mixed Implicit Quasi-variational Inequalities,then we prove the convergence of them, in g-Pseudomontone operation condition.In all,the results presented in this paper extend and improve many known results in the literature.