Banach空间中增生型变分包含解的Mann和Ishikawa迭代逼近

张石生

Banach空间中增生型变分包含解的Mann和Ishikawa迭代逼近

张石生

四川大学数学系, 成都 610064

基金项目: 国家自然科学基金课题(19971058)

详细信息

作者简介:
张石生(1934- ),男,教授.

中图分类号: O177.91
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- 被引次数: 0
出版历程
- 收稿日期: 1998-02-20
- 刊出日期: 1999-06-15

On the Mann and Ishikawa Iterative Approximation of Solutions to Variational Inclusions with Accretive Type Mappings in Banach Spaces

Zhang Shisheng

Department of Mathematics, Sichuan University, Chengdu 610064, P R China

摘要

摘要: 本文引入和研究Banach空间中一类增生型变分包含解的存在性及其Mann和Ishikawa迭代程序的收敛性问题。本文结果是张石生,丁协平,Hasouni,Kazmi,Siddiqi,Zeng的相应结果的改进和推广。
- 变分包含 /
- 增生映象 /
- Mann迭代序列 /
- Ishikawa迭代序列
Abstract: The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang,Ding, Hassouni, Kazmi, Siddiqi, Zeng,et al.
- variational inclusion /
- accretive mapping /
- Mann iterative sequence /
- Ishikawa iterative sequence

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参考文献(15)

[1]	Hassouni A, Moudafi A. A perturbed algorithm for variational inclusions[J].J Math Anal Appl,1994,185(3):706～721.
[2]	Ding Xieping. Perturbed proximal point algorithms for generalized quasivariational inclusions[J].J Math Anal Appl,1997,210(1):88～101.
[3]	Ding Xieping. Generalized strongly nonlinear guasivariational inegualities[J].J Math Anal Appl,1993,173(2):577～587.
[4]	Chang S S, Yuan X Z, Wang F. The study of algorithms and convergence for generalized multi-valued quasivariational inclusions[J].Topological Methods in Nonlinear Anal,(in print).
[5]	张石生.变分不等式和相补问题理论及应用[M].上海:上海科技文献出版社,1991.
[6]	Kazmi K R. Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions[J].J Math Anal Appl,1997,209(2):572～584.
[7]	Zeng L C. Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities[J].J Math Anal Appl,1994,187(2):352～360.
[8]	Noor M A. General variational inequalities[J].Appl Math Lett,1998,1(2):119～122.
[9]	Noor M A. An iterative algorithm for variational inequalities[J].J Math Anal Appl,1991,158(3):448～455.
[10]	Siddiqi A H, Ansari Q H. General strongly nonlinear variational inequalities[J].J Math Anal Appl,1992,166(2):386～392.
[11]	Siddiqi A H. Ansari Q H, Kazmi K R. On nonlinear variational inequalities[J].Indian J Pure Appl Math,1994,25(4):969～973.
[12]	游兆永,龚怀云,徐宗本.非线性分析[M].西安:西安交通大学出版社,1991.
[13]	Chang S S. On Chidume's open questions and approximate solutions for multi-valued strongly accretive mapping equations in Banach spaces[J].J Math Anal Appl,1997,216(1):94～111.
[14]	Liu L S. Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194(1):114～125.
[15]	Morales C. Surjectivity theorems for multi-valued mappings of accretive type[J].Comment Math Univ Carolina,1985,26。