Some Properties Of The Iterative Of Fixed Point

The problem of fixed point is one of the emphasis problems of people's regard and the corresponding research has gained many great achievements. Among many directions of the fixed point researches, it becomes main problem that the convergence problem about making approximating fixed point sequences and its application in control, nonlinear operator and derivative equation etc. The research of this problem will play an important role in its application in reality. In this paper, the Ishikawa and Mann iterative sequences are discussed and some properties of the convergence of the Ishikawa and Mann iterative processes with errors and their detail conclusion under different mappings are introduced.The paper consists of four parts. The main results of this paper are summarized as following:The development of the fixed point theory home and abroad is narrated in the preface and the main content that we will discuss, background and significance are introduced.Some definitions and related knowledge used in the article are introduced in the preparation, which is the arrangement to draw the conclusions.In the third chapter, the main results are given: the convergence problems of Ishikawa, general Ishikawa and Ishikawa iterative processes with errors under the strong accretive mapping (Φ- strongly accretive mapping), strong pseudo-contractive mapping (Φ- strongly pseudo-contractive mapping). In this chapter, some conclusions are extended to the real Banach space under different mappings, and a proof on the equivalence of Mann and Ishikawa iterative processes with errors under the uniformly pseudo-contractive mapping is given.In the forth chapter, the convergence problem of three Ishikawa and modified three Ishikawa iterative sequences under uniformly continuousΦ-strongly pseudo-contractive mapping and approximating pseudo-contractive mapping is...