Completely Generalized Mixed Implicit Quasi-Variational Inequality And A System Of Generalized Implicit Quasi Variational-Like Inclusion

In this paper, existence theorems of solutions and the convergence criteria of iterative algorithm for Completely Generalized Mixed Implicit Quasi-Variational Inequality and A System of Generalized Implicit Quasi Variational-Like Inclusion have been studied in Hilbert spaces.Firstly, we show the real background of the variational inequality theory and the main of works for Generalized Implicit Quasi Variational problems that have been studied by many authors, so as to show that our works worthy of attention. We also introduce some basic conceptions and our main results in this article.In the second chaper, by applying resolvent operator technique, an existence theorem of solutions for Completely Generalized Mixed Implicit Quasi-Variational Inequality involving strongly monotone,relaxed Lipschitz,subdifferential is proved in Hilbert spaces. A novel iterative algorithm to compute approximate solutions is suggested. The convergence criteria is also given.In the third chaper, by using the properties ofη-strongly monotone,(G,η)-monotone and generalized resolvent operator, A System of Generalized Implicit Quasi Variational-Like Inclusion has been studied in Hilbert spaces. The existence of solution and the convergence of iterative sequences have also been given by mann iterative.