<em>φ</em>-半压缩算子和<em>φ</em>-强增殖算子方程的迭代

丁协平; 张红琳

φ-半压缩算子和φ-强增殖算子方程的迭代

四川师范大学数学系, 成都 610066

基金项目: 国家自然科学基金资助项目(19871059)

详细信息

作者简介:
丁协平(1938- ),男,四川自贡人,教授,数学研究所所长.

中图分类号: O177.91
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- 被引次数: 0
出版历程
- 收稿日期: 1999-06-21
- 修回日期: 2000-09-20
- 刊出日期: 2000-11-15

Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P R China

摘要

摘要: 设E是任意实Banach空间,K是E的非空闭凸子集.T:K→K是一致连续φ-半压缩映像且值域有界.设{a_n},{b_n},{cn},{a'_n},{b'_n}和{c'_n}是[0,1]中的序列且满足条件:ⅰ)a_n+b_n+c_n=a'_n+b'_n+c'_n=1,∀n≥0; 对任意给定的x0,u0,v0∈K,定义Ishikawa迭代{x_n}如下:,其中u_n和v_n是K中两个有界序列.则xn强收敛于T的唯一不动点.最后研究了φ-强增殖算子方程解的Ishikawa迭代收敛性.
- φ-强增殖算子 /
- φ-半压缩算子 /
- Ishikawa迭代序列 /
- Banach空间
Abstract: Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E.Let T:K→K be a uniformly continuous φ-hemicontractive operator with bounded range and {a_n},{b_n},{cn},{a'_n},{b'_n},{c'_n}be sequences in[0,1] satisfying:ⅰ)a_n+b_n+c_n=a'_n+b'_n+c'_n=1,∀n≥0; For any given x0,u0,v0∈K,define the Ishikawa type iterative sequence {x_n} as follows: where {u_n} and {v_n} are bounded sequences in K.Then {x_n} converges strongly to the unique fixed point of T.Related result deals with the convergence of Ishikawa type iterative sequence to the solution of φ-strongly accretive operator equations.
- φ-strongly accretive operator /
- φ-hemicontrictive operator /
- Ishikawa type iterative sequence /
- Banach space

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参考文献(16)

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