The Applications Of Three-Step Iteration Method And Ishikawa Iteration Method With Errors To Convergence Of Fixed And Common Fixed Points For Nonlinear Mappings

In this paper, the convergences of three-step iteration method, generalized three-step iteration method and Ishikawa iteration method with errors for quasi-contractive mappings, generalized quasi-contractive mappings and a pair of quasi-contractive mappings in different spaces are established, respectively. In section three, two convergence results of three-step iteration method for quasi-contractive mappings in Hilbert spaces are established, an example is given to show that one of the results in this section extends the corresponding known result. In section four, the convergence theorems of three-step iteration method and generalized three-step iteration method for quasi-contractive and generalized quasi-contractive mappings in Banach spaces are obtained, respectively. It is clear that the previously corresponding results are special cases of results presented in this section. In section five, the convergence of common fixed points of Ishikawa iteration method with errors for a pair of quasi-contractive mappings in uniformly convex Banach spaces is proved. The results presented in this paper extend, improve and unify the corresponding known results in this field.