On a hybrid method for a family of relatively nonexpansive mappings in a Banach space
On a hybrid method for a family of relatively nonexpansive mappings in a Banach space
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DOI：
10.1016/j.jmaa.2009.03.052
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发表时间：
2009-09
影响因子：
1.3
通讯作者：
Y. Kimura;W. Takahashi
中科院分区：
文献类型：
--
作者：
Y. Kimura;W. Takahashi
在较弱的条件下，利用Takahashi，Takeuchi和Kubota给出的混合方法，证明了一类相对非扩张映象的强收敛定理。证明方法与原证明方法不同，表明迭代法中所用的投影类型与映射的性质无关。我们还讨论了求极大单调算子零点的问题，并利用这种方法得到了一个强收敛定理。
We prove strong convergence theorems by the hybrid method given by Takahashi, Takeuchi, and Kubota for a family of relatively nonexpansive mappings under weaker conditions. The method of the proof is different from the original one and it shows that the type of projection used in the iterative method is independent of the properties of the mappings. We also deal with the problem of finding a zero of a maximal monotone operator and obtain a strong convergence theorem using this method.