Iterative Methods For Nonlinear Accretive Nonexpansive Mappings In Banach Spaces

Solution of nonlinear equation x+Tx=f as one of the research problem of the fixed point theory,In this paper,we mainly study the iterative solution methods for m-accretive mapping and nonexpansive mapping fixed points in the Banach spaces and discuss the convergence of Mann and Ishikawa iterative methods.Mann iterative process is proved to strongly converge to the zero of m-accretive and nonexpansive mapping on a q-uniformly smooth Banach space.The first chapter is introduction.We mainly introduce the definition and classification of the mapping and the development course of iterative solution of equations in different spaces.The second chapter,we mainly introduce the convergence of Mann type iterative method for nonlinear equation x+Tx=f in Hilbert space.The third chapter,we mainly introduce the convergence of a Ishikawa type iterative method for nonlinear equation x+Tx=f in Hilbert space.By Offering different types of Banach space and conditions of the different types of operators,we obtain convergence and convergence theorems of the solutions.The fourth chapter mainly introduce monotone operators in the Lp(or lp)space,1<p<?,Mann and Ishikawa iterative methods approximation solution of nonlinear equations.Further more,this paper expands the convergence theorem of the above two chapters to in the Lp(or lp)space,1<p<?.The fifth chapter,we mainly introduce Mann iterative process strongly converge to the zero of m-accretive and nonexpansive mapping in the Banach space.This paper is to extend Dotson's convergence result from the Hilbert space setting to the setting of Banach spaces which are q-uniformly smooth for q ?(1,2].we will fill up this gap in a q-uniformly smooth Banach space.The sixth chapter mainly summarize the conclusion in this paper.