Iterative Methods For Nonlinear Operators

The fixed point theory of nonlinear op(?)rators is an constituent important part of nonlinear functional analysis, especially, the problem of approximating to solutions of nonlinear operator equations becomes the topic that people study in the recently years. Specially, nonlinear operator semigroups common fixed point theory is also an constituent important part of nonlinear functional analysis. For a rather long time, many authors have been using Hapern iterative methods and modified Mann iterative methods for computing solutions to nonlinear operator equations or the fixed points of nonlinear operators groups. In this paper, we have mainly used several different methods to do research on nonexpansive mappings semigroups, asymptotically pseudocontractive mappings semigroups, a finite family hemicontractive mappings, pseudocontractive mappings and nonexpansive mappings, and we have gained some strongly convergence theories. Results presented in this paper improve, extend and unify many authors's recent results. This paper includes five chapters. Now we will describe them briefly one by one. Chapter 1 states that present situation of iteration algorithms for solutions of nonlinear operator equations in Hilbert spaces and Banach spaces , and we also give a development stage of this work. Chapter 2 mainly concerns about iterative approximation problems for nonexpansive mappings semigroups. Chapter 3 mainly discusses about iterative approximation problems for asymptotically pseudocontractive mappings semigroups. Chapter 4 pays attention to iterative approximation problems for a finite family hemicontractive mappings. The last Chapter mainly considers approximating fixed points of pseudocontractive mappings and nonexpansive mappings in Banach space.