Variational Inclusions In Banach Spaces Existence Problems Of Solutions And Iterative Approximation

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, uniqueness, iterative approximation , and convergence and stability of iterative approximation of solutions to nonlinear variational inclusion problems.There are five chapters in this thesis.In Chapter 1, the author introduces the backgroud of variational inclusions and the main work of this thesis.In Chapter 2, some new convergence and stability theorems of the Ishikawa iterative procedures with errors for solutions to variational inclusions involving accretive mappings in real reflexive Banach space are proved.In Chapter 3, Some new convergence and stability theorems of the approximation methods of solutions to variational inclusions involving accretive mappings in real reflexive Banach space which is uniformly convex and q-uniformly smooth are proved.In Chapter 4, the author investigates the Mann-type iterative approximation problem of solutions for a class of variational inclusion problems with strongly accretive-type mappings in a real p-uniformly smooth Banach space.