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Completely Generalized Mixed Implicit Quasi-Variational Inequality and a System of Generalized Implicit Quasi Variational-Like Inclusion

Author: XiaoChengYing
Tutor: DengLei
School: Southwestern University
Course: Applied Mathematics
Keywords: Completely Generalized Mixed Implicit Quasi-Variational Inequality strong monotone Resolvent operator relaxed Lipschitz Lipschitz continuous (G,η)-monotone generalized resolvent operator mann iterative A System of Generalized Implicit Quasi Variational-Like Inclusion
CLC: O177.91
Type: Master's thesis
Year: 2008
Downloads: 16
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Abstract


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.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Nonlinear Functional Analysis
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