Banach空间中关于增生算子的强收敛迭代序列

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 755-759.

Banach空间中关于增生算子的强收敛迭代序列

崔欢欢

洛阳师范学院数学科学学院河南洛阳 471022

收稿日期:2012-10-08 修回日期:2014-03-06 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11301253)资助

An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces

CUI Huan-Huan

Department of Mathematics, Luoyang Normal University, Henan Luoyang 471022

Received:2012-10-08 Revised:2014-03-06 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11301253)资助

摘要/Abstract

摘要：

主要研究求解增生算子零点问题的一类算法: x_n₊₁=α_nu+(1-α_n)((1-λ)x_n+λJ_rnx_n), 其u是固定向量, λ∈(0,1), {r_n}和{α_n}是实数列, Jr_n表示增生算子A的预解式. 其中(r_n)收敛是保证算法收敛的一个充分条件, 该文主要证明了此条件可减弱为lim_n|1-r_n+1/r_n|=0.

关键词: 增生算子, 预解式, 弱连续对偶映像

Abstract:

This paper deals with the problem: find x so that 0∈Ax, where A is an accretive operator. One algorithm solving this problem has the following scheme: x_n₊₁=α_nu+(1-α_n)((1-λ)x_n+λJr_nx_n), where u is a fixed element, λ(0,1), {r_n} and α_n are real sequences, and Jr_n denotes the resolvent of A. The algorithm is known to converge provided that (r_n) is a convergent sequence. In this paper we show that such a condition can be relaxed as lim_n→∞|11-r_n+1/r_n|=0.

Key words: Accretive operator, Resolvent, Weakly continuous duality map

中图分类号:

47H06

崔欢欢. Banach空间中关于增生算子的强收敛迭代序列[J]. 数学物理学报, 2014, 34(3): 755-759.

CUI Huan-Huan. An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces[J]. Acta mathematica scientia,Series A, 2014, 34(3): 755-759.

[1]	曾六川. 关于增生算子方程解的带误差的Ishikawa迭代程序[J]. 数学物理学报, 2004, 4(6): 654-660.
[2]	谷峰. 一类非线性算子Ishikawa迭代序列的强收敛定理[J]. 数学物理学报, 2001, 21(1): 102-109.
[3]	柴国庆. Banach空间中一类非线性算子Ishikawa迭代序列收敛定理[J]. 数学物理学报, 1998, 18(4): 459-466.
[4]	张显文, 朱广田, 王绵森. 具积分边界条件的中子迁移方程的适定性及谱分布[J]. 数学物理学报, 1994, 14(1): 61-67.