Nonlinear Operator Equations Of Ishikawa And Mann Iterative Method

In this paper , we are concerned about Ishikawa and Mann iteration methods fornonlinear operator equations in Banach spaces which are very interesting and quiteimportant problems in the study of nonlinear approximation theory. For a rather longtime, many authors have been using Ishikawa and Mann iterative methods forcomputing solutions to nonlinear operator equations and fixed points of nonlinearoperators. So one topic of this thesis is to further study Ishikawa and Mann iterationmethods for solutions to nonlinear equations involving single-valued m ? accretive orset-valued accretive operators in Banach spaces. Another topic of this thesis is toconsider Ishikawa and Mann iteration methods for finding fixed points ofasymptotically hemicontractive type mappings in Hilbert spaces, since the fixedpoints problems of nonlinear operators are just nonlinear operator equations. Resultspresented in this paper improve, extend and unify many authors'recent 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 onIshikawa and Mann iteration methods for solving nonlinear operator equations inBanach spaces, and we also give a summary of this work.In Chapter 2, we mainly concern about iterative approximation problems withmixed errors for solutions to nonlinear equations involving m ? accretive operators inBanach spaces.In Chapter 3, we discuss Ishikawa and Mann iteration methods with mixed errorsfor solutions to nonlinear equations involving set-valued accretive operators.In the last chapter, we consider Ishikawa and Mann iterative approximationproblems for fixed points of asymptotically hemicontractive type mappings in Hilbertspaces.