Iterative Methods For System Of Variational Inequalities And Several Fixed Points Problems In Banach Space

Variational inequality problem is a very important research direction in the field of optimization,and it has a wide range of applications in engineering,economics,control theory and other fields.This paper improves the existing algorithms and proposes a hybrid viscosity extragradient method for system of variational inequalities,fixed points of nonexpansive mappings,and some optimization problems,and the strong convergence of the suggested algorithms are proved.The paper is divided into four parts:Chapter 1,we introduce the research background and research significance in this paper,recall the development history of variational inequalities and their current research status at home and abroad,and present the formulation about the main research work of this paper.Chapter 2,some related lemmas and propositions about variational inequalities are presented.On the basis of the existing literature,the corresponding algorithm is improved,The implicit iterative method for the system of variational inequalities,the fixed point problem and the zero point problem of accretive operators in Banach space is obtained,and its strong convergence is proved.Then,we propose the explicit iteration method for the system of variational inequalities,fixed point problems,and variational inequality problems in Banach space,and prove the strong convergence of the algorithm.Chapter 3,first,we recall some related lemmas about the equilibrium problem,and improve the existing algorithm.Based on the framework of chapter 2,we suggest the explicit iterative method for variational inequalities system,fixed point problem and equilibrium problem,and analyze its strong convergence.Chapter 4,we give the conclusion and outlook of this paper.