The Study Of Solutions To Nonlinear Variational Inclusions

Variational inequality is an important part of nonlinear analysis theory, and variational inclusions are key generalizations of variational inequalities. The purpose of the paper is to discuss the existence, uniqueness, convergence of algorithms, and iterative approximation of solutions to nonlinear variational inclusion problems. The results presented in this paper improve and extend some corresponding results.This paper includes four chapters. Now we will describe them briefly one by one.In chapter 1, we recall the history and introduce the backgrounds of the research on nonlinear variational inclusions and the main work of this thesis.In chapter 2, we study a class of variational inclusions with pseudocontraction type. The convergence analysis of the Ishikawa iterative procedure with errors for finding solutions to this class of variational inclusions is presented in a real reflective Banach space.In chapter 3, we discuss a class of variational inclusions withΦ-Pseudocontraction type. The convergence analysis of the Ishikawa iterative procedure with errors for finding solutions to this class of variational inclusions is presented in a real p-uniformly smooth Banach space. The results improve and develop the earlier and recent corresponding ones in the literature.In the last chapter, in Banach space,by using the resolvent operator technique, we anal-yse a new system of set-valued mixed quasi-variationan-like inclusions involing generalized m-accretive mappings and construct some algorithms for approximating the solution of this class of variational inclusions with generalized m-accretive mappings.