Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代程序的收敛性问题

张石生

Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代程序的收敛性问题

张石生

四川大学数学系, 成都 610064

基金项目: 国家自然科学基金资助课题(19971058)

详细信息

作者简介:
张石生(1934~ ),男,教授,已发表论文290余篇,获省部级奖6项.

中图分类号: O177.91
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- 文章访问数: 2071
- HTML全文浏览量: 120
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- 被引次数: 0
出版历程
- 收稿日期: 1998-08-07
- 修回日期: 1999-06-09
- 刊出日期: 2000-01-15

On the Convergence Problems of Ishikawa and Mann Iterative Processes With Error for Φ-Pseudo Contractive Type Mappings

Zhang Shisheng

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

摘要

摘要: 引入Φ-伪压缩型映象的概念,并研究了此类映象的具误差的Ishikawa和Mann迭代程序的收敛性问题.本文结果改进和发展了许多人的最新结果.
- Φ-伪压缩型映象 /
- 增生映象 /
- 伪压缩映象 /
- Φ-强增生映象 /
- Φ-半压缩映象 /
- 具误差的Ishikawa迭代程序 /
- 具误差的Mann迭代程序
Abstract: The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings.The results presented in this paper improve and extend many authors' recent results.
- Φ-pseudo contractive type mapping /
- accretive mapping /
- pseudo-contractive mapping /
- Φ-strongly accretive mapping /
- Φ-hemi-contractive mapping /
- Ishikawa iterative processes with error /
- Mann iterative process with error

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参考文献(24)

[1]	Dunn J C.Iterative construction of fixed points for multivalued operators of the monotone type[J].J Functi Anal,1978,27,38～50.
[2]	Chidume C E.Iterative construction of fixed points for multivalued operators of the monotone type[J].Appl Anal,1996,23:20 9～218.
[3]	Chang S S,Tan K K.Iteration processes of fixed point for operators of monotone type in Banach spaces[J].Bull Austral Math Soc,1998,57:433～445.
[4]	Osilike M O.Iterative solution of nonlinear equations of the φ-strongly accretive type[J].J Math Anal Appl,1996,200:259～271.
[5]	Browder F E.Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J].Bull Amer Math Soc,1967,73:875～882.
[6]	Kato T.Nonlinear semi-groups and evolution equations[J].J Math Soc Japan,1964,19:508～520.
[7]	Ishikawa S.Fixed point by a new iteration method[J].Proc Amer Math Soc,1974,14(1):147～150.
[8]	Mann W R.Mean value methods in iteration[J].Proc Amer Math Soc,1953,4:506～510.
[9]	Chang S S.On Chidume's open questions and approximate solutions of multivalued strongly accretive mappings equations in Banach spaces[J].J Math Anal Appl,1997,216:94～111.
[10]	Chang S S.Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal,1997,30(7):4197～4208.
[11]	Chidume C E.Approzimation of fixed points of strongly pseudo-contractive mappings[J].Proc Amer Math Soc,1994,120(2):545～551.
[12]	Chidume C E.Steepest descent approximations for accretive operat or equations[J].Nonlinear Anal,1996,26:299～311.
[13]	Chidume C E.Iterative solution of nonlinear equations with stron gly accretive operators[J].J Math Anal Appl,1993,192:50 2～518.
[14]	Chidume C E,Osilike M O.Ishikawa process for nonlinear Lipschitz strongly accretive mappings[J].J Math Anal Appl,1995,192:727～741.
[15]	Deng Lei.On Chidume's open questions[J].J Math Anal Appl,1993,174(2):441～449.
[16]	Deng Lei,Ding Xieping.Iterative approximation of Lipschitz striongly pseudo-contractive mappings in uniformly smooth Banach spaces[J].Nonli near A nal,1995,24:981～987.
[17]	Osilike M O.Stable iteration procedures of strong pseudo-contractions and nonlinear operator equations of the accretive type[J].J Math Anal Appl,1996,204:677～692.
[18]	Osilike M O.Iterative construction of fixed points of multi-valued operators of the accretive type[J].Soochow J Math,1996,22(4):485～494.
[19]	Reich S.An iterative procedure for constructing zeros of accretive sets in Banach spaces[J].Nonlinear Anal,1978,2:85～92.
[20]	Reich S.Strong convergence theorems for resolvents of accretive operators in Banach spaces[J].Math Anal Appl,1980,85:287～292.
[21]	Tan K K,Xu H K.Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces[J].J Math Anal Appl,1993,178:9～21.
[22]	Zhou H Y.Remarks on Ishikawa iteration[J].Chinese Sci Bull,1977,42:126～128.
[23]	Liu L S.Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194:114～125.
[24]	Zeidler E.Nonlinear Functional Analysis and Its Applications[M].Part Ⅱ,Monotone Operators,New York/Berlin:Springer-Verlag,1985