A Class Of Implicit Iterative Scheme For Approximating Fixed Points Of Nonexpansive Mappings And Strictly Pseudocontractive Mappings

Fixed point iterative algorithms of nonlinear operators is the product which functional analysis and computational mathematics combine. In the recent 10 years, as a result of scientific research and engineering practice to stimulate strongly, as well as the rapid development of modern computers to promote powerfully, fixed point iterative algorithms of nonlinear operators obtain the rapid development, and become one of hot spots in functional analysis and computational mathematics research. The nonexpansive mapping is the most important one of the nonlinear operators. The fixed point iterative algorithm of nonexpansive mapping has accumulated systematic research results. The core of this article is based on the guiding ideology to improve the convergence rate of the present iterative algorithms, construct a new class of implicit iterative scheme for approximating fixed points of nonexpansive and strictly pseudo-contractive mappings, and improve the availability of similar results. The specific content of this paper mainly include the following three aspects:Firstly, for nonexpansive mappings, a new implicit iteration scheme is introduced, and the convergence property is strictly proved. This scheme improve the convergence rate.Secondly, using metric projected method, we improve the implicit iterative scheme that is proposed by Zhao, He, and Su, and still prove the strong convergence theorems without the hypothesis of compactness of nonexpansive operators.Finally, the mentioned format is applied to approximating the fixed point of strictly pseudo-contractive mappings, several convergence theorems are obtained, many existing results has been improved.