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STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES
  • ISSN号：1009-6124
  • 期刊名称：《系统科学与复杂性学报：英文版》
  • 时间：0
  • 分类：O152.7[理学—数学;理学—基础数学]
  • 作者机构：[1]Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
  • 相关基金：This research is supported by the National Natural Science Foundation of China under Grant No. 10771050.
作者： Yongfu SU Xiaolong QIN[1]
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
中文摘要：

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。

英文摘要：

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.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
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  • 被引量:125