非线性Φ伪压缩映象不动点的具误差的迭代过程

数学物理学报 ›› 2004, Vol. 4 ›› Issue (6): 730-736.

非线性Φ伪压缩映象不动点的具误差的迭代过程

徐裕光

昆明师范高等专科学校数学系

出版日期:2004-12-25 发布日期:2004-12-25
基金资助:
本项工作由国家自然科学基金(19961004)和云南省自然科学基金资助

Iterative Processes with Errors for Fixed Points \=of Nonlinear |ΦPseudocontractive Mappings

XU Yu-Guang

Online:2004-12-25 Published:2004-12-25
Supported by:
本项工作由国家自然科学基金(19961004)和云南省自然科学基金资助

摘要/Abstract

摘要：

该文的目的是要引入比重要的强伪压缩映象更一般的Φ伪压缩映象，并且在更一般的假设下，用具误差的 Ishikawa和 Mann迭代过程去研究这类映象不动点的迭代逼近问题。研究结果表明：Φ伪压缩映象T的一致连续性保证了在任意实Banach空间E中，Ishikawa迭代序列强收敛于T的唯一不动点；进一步，如果E是一致光滑的则T的连续性是不必要的

关键词: Φ伪压缩映象, 强伪压缩映象, 具误差的Ishikawa迭代过程, 具误差的Mann迭代过程

Abstract:

The purpose of this paper is to introduce Φpseudocontractive mappings-aclass of mappings which is much more general than the important class of　strongly pseudocontractive mappings and to study approximate problems of fixed point for the mappings by Ishikawa and Mann iterative processes with errors in more general settings. The results presented in this paper show that the uniformly continuity of mapping T ensures the Ishikawa iterative sequence converges strongly to unique fixed point of T in a Banach space X; if X is uniformly smooth then the continuity of T is not necessary.

Key words: Φpseudocontractive mapping, strongly pseudocontractive mapping, Mann iteration sequence, Ishikawa iteration sequence

中图分类号:

47H09

徐裕光. 非线性Φ伪压缩映象不动点的具误差的迭代过程[J]. 数学物理学报, 2004, 4(6): 730-736.

XU Yu-Guang. Iterative Processes with Errors for Fixed Points \=of Nonlinear |ΦPseudocontractive Mappings[J]. Acta mathematica scientia,Series A, 2004, 4(6): 730-736.

参考文献

[1］Asplund E. Positivity of duality mappings. Bull Amer Math Soc, 1967, 73: 200-203

[2］Ishikawa S. Fixed point and iteration of a nonexpansivemapping in a Banach spaces. Proc Amer Math Soc, 1976, 73: 65-71
［3］Mann W R. Mean value methods in iteration.Proc Amer Math Soc, 1953, 4: 506-510
［4］ Xu Y. Ishikawa and Mann iterative processes witherrors for nonlinear strongly accretive operator equations.J Math Anal Appl, 1998, 224: 91-111
［5］Chidume C E. Approximation of fixed points of strongly pseudocontractive mappings. Proc Amer Math Soc, 1994, 120: 545-551
［6］ Chang S S. On chidume's open questions and approximation solutions of multivalued strongly accretive mapping equations in Banach
spaces. J Math Anal Appl, 1997, 216: 94-111
［7］ Chang S S, Cho Y J, Lee B S, Kang S M. Iterativeapproximations of fixed points and solutions for strongly accretive andstrongly pseudocontractive mappings in Banach spaces.J Math Anal Appl, 1998, 224: 149-165
［8］Liu L S. Ishikawa and Mann iterative process with errors fornonlinear strongly accretive mappings in Banach spaces.J Math Anal Appl, 1995, 194: 114-125
［9］ Zhou H. Some convergence theorems for the Ishikawa iterative sequences of certain nonlinear operators in uniformly smooth Ba

nach spaces. Acta Math Sinica,1997, 40: 751-758
［10］Chang S S. On the convergence problems of Ishikawa and Mann iterative processes with error for Φpseudo
contractive type mappings. Applied Mathematics and Mechanics, 2000,21: 11-16
［11］Chai Guoqing. Some convergence theorems for iterative sequence of certain nonlinear in Banach space. Acta Math ematica scientia, 1998, 18: 459-466
［12］Chidume C E. Iterative solutions of nonlinear equations insmooth Banach spaces. Nonlinear Anal, 1996, 26: 1823-1834
［13］Chidume C E, Osilike M O. Fixed point iterations forstrictly hemicontractive maps in uniformly smooth Banach spaces.Numer Funct Optim, 1994, 15: 779-790
［14］Chidume C E, Moore. The solution by iteration of nonlinear equations in uniformly smooth Banach spaces. J Math Anal Appl, 1997, 215: 132-146
［15］Chidume C E. Global iteration schemes for strongly pseudocontractive maps. Proc Amer Math Soc, 1998, 126: 2641-2649
［16］Chidume C E. Convergence theorems for strongly pseudocontractiveand strongly accretive maps. J Math Anal Appl, 1998, 228: 254-264
［17］Deng L, Ding X P. Iterative approximation ofLipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces. Nonlinear Anal TMA,1995, 24: 981-987
［18］ Ding X P. Iterative process with errors to locallystrictly pseudocontractive maps in Banach spaces, Computers Math Applic, 1996, 32: 91-97
［19］ Ding X P. Iterative process with errors to nonlinearΦstrongly accretive operator equations in arbitrary Banach spaces. Computers Math Applic, 1997, 33: 75-82
［20］ Osilike M O. Iterative solutions of nonlinearstrongly accretive operator equations in arbitrary Banach spaces.Nonlinear Analysis, 1999, 36: 1-9
［21］ Liu Zeqing, Kang S M. Convergence theorems for strongly accretive and hemicontractive operators. J Math Anal Appl, 2001, 253: 35-49
［22］ Browder F E. Nonlinear operations and nonlinear equationsof evolution in Banach spaces. Proc Sympos Pure Math, 1976