Iterative Approximation Problems Of Fixed Points For Nonlinear Operators

This paper deals with the iterative approximation problems of fixed points for non-linear operators in Banach spaces which are always one of the best important problems in the nonlinear approximation theory. For a long time, many authors have been using Mann and Ishikawa iterative methods for finding fixed points of nonlinear operators. On one hand, we consider iterative approximation of common fixed points for a pair of asymptotically nonexpansive nonself-maps and iterative approaches to fixed points of uniformly Lipschitzian mappings in Banach spaces. On the other hand, we study strong convergence of modified Ishikawa three-step iterative sequences with errors for three nonexpansive mappings. The results presented in this paper improve, extend and develop some recent corresponding 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 the 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 mainly concern about iterative approximation of common fixed points for a pair of asymptotically nonexpansive nonself-maps.In Chapter 3, we study strong convergence of modified Ishikawa three-step iterative sequences with errors for nonexpansive mappings.In the last chapter, we discuss iterative approaches to fixed points of uniformly Lipschitzian mappings in Banach spaces.