Iterative Approximation Problems Of Fixed Points For Nonlinear Operators

This paper deals with the iterative approximation problem of fixed points for non-linear operators in Banach spaces which is always one of the best important problemsin the nonlinear approximation theory. For a long time, many authors have been usingMann and Ishikawa iterative methods for finding fixed points of nonlinear operators.On one hand, we consider iterative schemes for finitely many asymptotically pseudocon-tractive mappings in Banach spaces and convergence rate estimate of Ishikawa iterationmethod for m-accretive operators. On the other hand, we study iterative approximationfor asymptotically strict pseudocontractions in Hilbert spaces. The results presentedin this paper improve, extend and develop some recent corresponding results in theliterature.This paper includes four chapters. Now we will describe them brie?y one by one.In Chapter 1, we recall the history and present the situation of the research onIshikawa and Mann iteration methods for finding fixed points of nonlinear operators inBanach space, and we also give a summary of this work.In Chapter 2, we mainly concern about iterative schemes for finitely many asymp-totically pseudocontractive mappings in Banach spaces .In Chapter 3, we study convergence rate estimate of Ishikawa iteration method form-accretive operations. Finally, we study strong convergence of modified Mann iteration for asymptoticallystrict pseudocontractions in Hilbert spaces.