The Studies Of Accretive And Contractive Operators And Asymptotically Nonexpansive Mappings

The fixed point theory of nonlinear operations are important parts of nonlinear func-tional analysis. Especially, the problem of approximating to solutions of nonlinear operatorequations becomes the topic that people study in the recently years. In this paper, we in-troduce effective schemes with Meir-Keeler contractions for an m-accretive operator and anasymptotically nonexpansive mapping, and find a common element of the set of commonfixed points of a finite family of λi-strictly pseudo-contractions. Results presented in thispaper improve and extend many authors’recent results. This paper includes fives chapters.Now we will describe them briefly one by one.Chapter1In this chapter，we introduce the history and present situation of nonlinearoperator equations in Banach spaces and we also give a summary of this work.Chapter2We introduce the convergence problems of an m-accretive operator withMeir-Keeler contractions in Banach spaces.Chapter3We present the convergence of implicit and explicit schemes for an asymptot-ically nonexpansive mapping with MKC in q-uniformly smooth and strictly convex Banachspaces.Chapter4We discuses about the common fixed points of strict pseudocontractions byiterative algorithms in Hilbert spaces.