Banach空间中一类非线性算子Ishikawa迭代序列收敛定理

数学物理学报 ›› 1998, Vol. 18 ›› Issue (4): 459-466.

Banach空间中一类非线性算子Ishikawa迭代序列收敛定理

柴国庆

湖北师范学院数学系黄石 435002

收稿日期:1997-12-23 出版日期:1998-12-26 发布日期:1998-12-26

Some convergence Theorems for Iterative Sequence of Certain Nonlinear Operator in Banach Space

Chai Guoqing

Department of Mathematics, Hubei Normal College, Huang Shi 435002

Received:1997-12-23 Online:1998-12-26 Published:1998-12-26

摘要/Abstract

摘要： 在一般的Banach空间中,研究了Ishikawa迭代序列收敛问题,去掉了通常文献中关于空间X的一致光滑或S-一致光滑的严格要求,此外,还去掉或减弱了其它某些条件.因而本质地改进了近期文献^[1-7]的一系列相应定理.

关键词: Ishikawa迭代, 局部强增生算子, 局部强伪压缩算子

Abstract: In this paper, by a new technique, the author study the problem for the Ishikawa iterative sequence in the general Banach space, and obtains some new results, removes the strict condign of the space being uniformly smooth as usual, in addition, removes or weakens the other some condition, and so improves a series of corresponding theorems in recent pa-pers ^[1-7].

Key words: Ishikawa iteration, (local) Strongly accretive operator, (local) Strongly pseudocontractive operator

柴国庆. Banach空间中一类非线性算子Ishikawa迭代序列收敛定理[J]. 数学物理学报, 1998, 18(4): 459-466.

Chai Guoqing. Some convergence Theorems for Iterative Sequence of Certain Nonlinear Operator in Banach Space[J]. Acta mathematica scientia,Series A, 1998, 18(4): 459-466.

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[2]	. 逼近Banach空间中渐近非扩张映象的不动点[J]. 数学物理学报, 2003, 23(1): 31-37.
[3]	曾六川. 一致Banach空间中非扩张映象的弱收敛定理[J]. 数学物理学报, 2002, 22(3): 336-341.
[4]	曾六川. Banach空间中强增生型变分包含解的具误差的Ishikawa迭代逼近[J]. 数学物理学报, 2002, 22(1): 99-106.
[5]	谷峰. 一类非线性算子Ishikawa迭代序列的强收敛定理[J]. 数学物理学报, 2001, 21(1): 102-109.