Iterative Algorithms For Solutions Of Nonlinear Operator Equations

The fixed point theory of nonlinear operators is an 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. In this paper, we are concerned about Ishikawa and Mann iteration methods for nonlinear operator equations in Banach spaces which are very interesting and quite important problems in the study of nonlinear approximation theory. For a rather long time, many authors have been using Ishikawa and Mann iterative methods for computing solutions to nonlinear operator equations which are the fixed points of nonlinear operators. So one topic of this thesis is to modify Mann and Ishikawa iteration methods for nonexpansive mappings, asymptotically nonexpansive mappings, strict pseudocontractions, strictly asymptotically pseudocontractive maps and m-accretive operators and so on to have strong convergence by two different methods in Banach spaces and Hilbert spaces, respectively. Another topic of thesis is to consider multi-step Noor iteration methods for funding fixed points of nonself mappings in Banach spaces. The last topic of thesis is to use viscosity methods to approximate zero points of accretive operators. Results presented in this paper improve, extend and unify many authors' recent results. This paper includes five chapters. Now we will describe them briefly one by one.Chapter 1 recalls the history and present situation of nonlinear operator equations in Banach spaces, and we also give a summary of this work.Chapter 2 mainly concerns about iterative approximation problems for nonexpansive mappings and asymptotically nonexpansive mappings.Chapter 3 mainly discusses about iterative approximation problems for nonexpansive nonself mappings and asymptotically nonexpansive nonself mappings.Chapter 4 pays attention to iterative approximation problems for pseudo-contraction type mappings.The last Chapter mainly considers approximating zeros points of accretive operators.