Nonlinear Operator In The Banach Space Fixed Point Iterative Method

In this paper,we investigate the iteration methods for fixed points of nonlinear operators in Banach spaces.The iterative approximation of fixed points of nonlinear operators has always been being a very important problem in the study of nonlinear approximation theory.As we know,since the concept of asymptotically nonexpansive mappings came out ,many authors have considered and developed them in various ways.we introduce two new implicit iterative processes for.this class of nonlinear operator and prove the convergence.In addition,we also discuss the iterative approximation problem of nonlinear strongly accretive operator.This paper includes four chapters.Now we will describe them briefly one by one .In Chapter l,we recall the history and present situation of the research on the iteration methods for fixed points of nonlinear operators in Banach spaces,and we also give a summary of this paper.In Chapter 2,we introduce a new implicit iterative process and study the convergence of it to common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces.In Chapter 3,we discuss convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings which is also introduced by us.In Chapter 4,we mainly concern about iterative approximation theorem on solutions to nonlinear strongly accretive operator equations.