Iterative Algorithm And Convergence Analysis For Systems Of Variational Inequalities

In this paper, we study various forms systems of variational inequalities andvariational inclusions in Hilbert and Banach spaces respectively. By using themethods of projection operator, resolvent operators and others, we discuss thetheorems of the existence and convergence of the solution for systems of variationalinequalities and variational inclusions, and at the same time, we give thecorresponding iterative algorithm. Specific contents are as follows:In the first and second sections, we gave an introduction of related questionsand preliminary knowledge in Hilbert space.In the third one, a system of generalized variational inequalities involvingrelaxed co-coceive is discussed in the framework of real Hilbert spaces byutilizing the method of three-step projection. Furthermore, we give the iterativealgorithm with the error estimation and establish the theorems of the existence andthe convergence of the iterative sequences.In the fourth part, we discuss a system of quasi-like variational inclusions inreal Hilbert spaces. A new iterative scheme is given through using the method ofthe resolvent operator technique, and the strong convergence theorem of the systemof this variation inclusions is obtained.In the fifth section, we gave an implicit iterative algorithm for a system ofgeneralized variational inequalities in the framework of the real2-uniformly smoothBanach spaces by applying the sunny nonexpansive retraction mapping Q_k.Also,the convergence theorem is given.In the last division, we discuss a system of variational inclusions involving(H,η)-accretive operator in real q-uniformly smooth Banach spaces.Theequivalent operator equation of the variational inclusions is given by using thetechnique of the resolvent operator. Apart from that, we introduce a newcorresponding iterative process and the theorems of the existence and convergenceare established.Results proved in this paper may be viewed as improvement and refinement ofthe previously known results, such as[1-4,27-29]...