The Existence And Iterative Approximation Of Solutions To Several Classes Of Nonlinear Variational Inclusions

Theory of variational inequality is an important part of nonlinear functional analysis,and variational inclusions are generalizations of variational inequalities. The purpose of the paper is to discuss the existence and uniqueness of solutions to no nline arvariational inc lusions.The re sults presented in this paperimprove and extend some corre sponding re sults in the lite rature.There are four chapters in this thesis.Now we will describe them briefly one by one.In chapter l,the author introduces the background of nonlinear variatio nalinc lusio ns a nd the ma in work o f this the sis.In chapter2,we study a viscosity iteration method for hierarchial fixed point and variational inequalities. By the new iteration method,-some convergence theoremsare proved.In chapter3,we study approximation of solutions to a system of variational inclusions in Banach spaces.we propose and analyze a hybrid iteration scheme for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings.Strong convergence are established in uniformly convex and2-uniformly smooth Banach spaces.In chapter4,we introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings and monotone mappings in a Hilbert space.We obtain one strong convergence theorem.Utilizing this theorem, we drive some corollaries.