拟- Φ -渐近非扩张映像的修改的Halpern-Mann-型迭代的强收敛定理及应用

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1151-1160.

拟- Φ -渐近非扩张映像的修改的Halpern-Mann-型迭代的强收敛定理及应用

唐永昆¹, 张石生^1**, 王林¹, 徐裕光², 王刚¹

1.云南财经大学统计数学学院昆明 |650221|
2.昆明学院数学学院 |昆明 |650214

收稿日期:2012-09-28 修回日期:2013-12-18 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11361070)资助.

Strong Convergence Theorems of Modified Halpern-mann-type Iterations for Quasi-Φ-asymptotically Nonexpansive Mappings and Applications

TANG Yong-Kun¹, ZHANG Shi-Sheng^1**, WANG Lin¹, XU Yu-Guang², WANG Gang¹

1.College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221;
2.Department of Mathematics, Kunming University, Kunming 650214

Received:2012-09-28 Revised:2013-12-18 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11361070)资助.

摘要/Abstract

摘要：

该文的目的是修改拟- Φ -渐近非扩张映像的Halpern-Mann-型迭代算法. 并证明, 仅在一极限条件下, 该迭代算法在Banach 空间的框架下具有强收敛性. 结果改进和推广了文献[4, 6--7, 11--13]以及其他一些人的最新结果.

关键词: 修改的 Halpern-Mann-型迭代, 拟- Φ -渐近非扩张映像, 拟- &Phi, -非扩张映像, 相对非扩张映像, 广义投影

Abstract:

The purpose of this article is to modify the Halpern-Mann-type iteration algorithm for quasi-Φ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results of [4, 6--7, 11--13] and others.

Key words: Modified Halpern-Mann-type iteration, Quasi-Φ-symptotically nonexpansive map-pin, Quasi-Φ-nonexpansive mapping, Relatively nonexpansive mapping, Generalized projec-tion
MR(2000) Subject Classification: 47J05, 47H09, 49J25

中图分类号:

47J05

唐永昆, 张石生, 王林, 徐裕光, 王刚. 拟- Φ -渐近非扩张映像的修改的Halpern-Mann-型迭代的强收敛定理及应用[J]. 数学物理学报, 2014, 34(5): 1151-1160.

TANG Yong-Kun, ZHANG Shi-Sheng, WANG Lin, XU Yu-Guang, WANG Gang. Strong Convergence Theorems of Modified Halpern-mann-type Iterations for Quasi-Φ-asymptotically Nonexpansive Mappings and Applications[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1151-1160.

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