Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

曾六川

Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

曾六川

上海师范大学数学系, 上海 200234

基金项目: 高等学校优秀青年教师教学和科研奖励基金资助项目;上海市高等学校科学技术发展基金资助项目;上海市科委重大项目基金资助项目

详细信息

作者简介:
曾六川(1965- ),男,湖南人,教授,博士,博士生导师,已发表论文70余篇(E-mail:zenglc@hotmail.com).

中图分类号: O177.91
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出版历程
- 收稿日期: 2001-07-24
- 修回日期: 2003-06-27
- 刊出日期: 2003-12-15

Iterative Approximation of Fixed Points for Almost Asymptotically Nonexpansive Type Mappings in Banach Spaces

ZENG Lu-chuan

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

摘要

摘要: 在Banach空间中引入了一类新的几乎渐近非扩张型映象,概括了Banach空间中若干熟知的非线性的Lipschitz映象类与非Lipschitz映象类成特例;例如,熟知的非扩张映象类,渐近非扩张映象类与渐近非扩张型映象类.考虑了用于逼近几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的收敛性问题.关于Banach空间范数的S.S.Chang的不等式与H.K.Xu的不等式皆被用于做精确不动点与近似不动点间的误差估计.而且,张石生教授用于做带误差的修改了的Ishikawa迭代序列收敛性分析的方法(应用数学和力学,2001,22(1):23-31)被推广到几乎渐近非扩张型映象的情况.给出了用于求一致凸Banach空间中几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的新的收敛判据.并且,由该判据,立即得到了此类映象的带误差的修改了的Mann迭代序列的新的收敛判据.上述结果统一、改进与推广了张石生教授关于用带误差的修改了的Ishikawa与Mann迭代序列来逼近渐近非扩张型映象不动点方面的结果.
- 几乎渐近非扩张型映象 /
- 不动点 /
- 带误差的修改了的Ishikawa迭代序列 /
- 带误差的修改了的Mann迭代序列
Abstract: A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example, the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang's inequality but also H. K. Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, ZHANG Shi-sheng's method(Applied Mathema tics an d Mechanics(English Edition), 2001, 22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize ZHANG Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
- almost asympt otically nonexpansive type mapping /
- fixed point /
- modified Ishikawa iterative sequence with error /
- modified Mann iterative sequence with error

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参考文献(13)

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