Banach空间中含强增生算子的非线性方程的迭代解

周海云

Banach空间中含强增生算子的非线性方程的迭代解

周海云

军械工程学院基础部, 石家庄 050003

详细信息

作者简介:
周海云(1958~ ),男,副教授,已在国内外重要杂志上发表论文38篇

中图分类号: O177.91
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出版历程
- 收稿日期: 1997-04-28
- 修回日期: 1998-04-05
- 刊出日期: 1999-03-15

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces

Zhou Haiyun

Department of Basic Science, Ordnance Engineering College, Shijiazhuang 050003, P. R. China

摘要

摘要: 设X为实Banach空间,X^*为其一致凸的共轭空间.设T:X→X为Lipschitzian强增生映象,L≥1为其Lipschitzian常数,k∈(0,1)为其强增生常数.设{α_n},{β_n}为[0,1]中的两个实数列满足:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ).假设为X中两序列满足:=o(β_n)与μ_n→0(n→∞).任取x₀∈X,则由(IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0){所定义的迭代序列{x_n强收敛于方程T
- 带误差的Ishikawa迭代 /
- 强增生映象 /
- φ-半压缩映象
Abstract: :Let X be a real Banach space with a uniformly convex dual X^*. Let T :X y X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L≥1 and a strongly accretive constant k∈(0,1). Let {α_n},{β_n}. be two real sequence in [0,1] satisfying:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ) Set Sx=f-Tx+x Assume that be two sequences in X satisfying =o(β_n)与μ_n→0(n→∞).For arbitrary x₀∈X the iteration sequence {x_n} is defined by IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0) then {x_n converges strongly to the unique solution of the equation Tx=f A related result deals with iterative approximation of fixed points of φhemicontractive mappings.
- Ishikawa iteration with errors /
- strongly accretive mapping /
- φ-hemicontractive mapping

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参考文献(32)

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