摘要
K。Nakajo 和 W。在 2003 的 Takahashi 由在数学编程使用混合方法在 Hilbert 空格为单调操作符的零个点为非广泛的地图砰，非广泛的半组，和近似的点算法证明了强壮的集中定理。这篇论文的目的是修改 K 的混合重复方法。Nakajo 和 W。通过单调混血儿方法的 Takahashi，并且证明集中定理强壮。单调混血儿方法的重复过程的集中率比 K 的混合方法的重复过程的快。Nakajo 和 W。Takahashi。在在这篇文章的证明， Cauchy 顺序方法被用来避免 demiclosedness 原则和 Opial 的条件的使用。
K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial＇s condition.
基金
This research is supported by the National Natural Science Foundation of China under Grant No.10771050
关键词
混合模型
不放大映射
不放大半群
近点算法
强收敛性
Hybrid method, nonexpansive mapping, nonexpansive semigroup, proximal point algorithm, strong convergence
