Iterative Approximation Problems For Nonlinear Operators In Banach Spaces

The purpose of this thsis is to investigate the iterative approximation problems for nonlinear operators in Banach spaces. The convergence problems of iterative sequences for nonlinear operators are always one of the best important problems in the nonlinear approximation theory. For a rather long time, many authors have been using Ishikawa and Mann iterative methods for finding fixed points of nonlinear operators and solutions to nonlinear operator equations. On one hand, we continue to study Ishikawa and Mann iteration methods for finding fixed points of finitely many set-valued mappings and finite family of asymptotically hemicontractive mappings. On the other hand, we continue to consider Ishikawa and Mann iteration methods for computing solutions to generalized Lipschitzian weekΦ-accretive operator equations, since the fixed points problems of nonlinear operators are just nonlinear operator equations. The results presented in this paper improve, extend and unify some authors' recent results.This paper includes four chapters. Now we will describe them briefly one by one.In chapter 1, we recall the history and present situation of research on Ishikawa and Mann iteration methods for finding fixed points of nonlinear operators in Banach space, and we also give a summary of this work.In chapter 2, we discuss the modified Mann iteration procedure for common fixed points of finitely many set-valued mappings. In chapter 3, we mainly concern about iterative approximation of solutions for generalized Lipschitzian weekΦ-accretive operator equations.In the final chapter, we conside the strong convergence of the iteration processes for a finite family of asymptotically hemicontractive mappings.