A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
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DOI：
10.1090/s0002-9939-06-08435-8
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发表时间：
2006-06
期刊：
影响因子：
--
通讯作者：
Tomonari Suzuki
中科院分区：
文献类型：
--
作者：
Tomonari Suzuki
本文证明了范数一致Gâteaux可微的Banach空间中非扩张映象的Halpern型强收敛定理。并讨论了该定理成立的充要条件。这是对赖希在1983年提出的问题的部分回答。
In this paper, we prove a Halpern-type strong convergence theorem for nonexpansive mappings in a Banach space whose norm is uniformly Gâteaux differentiable. Also, we discuss the sufficient and necessary condition about this theorem. This is a partial answer of the problem raised by Reich in 1983.