Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings
Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings
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DOI：
10.1137/050624315
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发表时间：
2006-01-01
影响因子：
3.1
通讯作者：
Takahashi, W
中科院分区：
文献类型：
--
作者：
Nadezhkina, N;Takahashi, W
本文介绍了寻找非扩张映象不动点集的公共元素和单调Lipschitz连续映象的变分不等式问题解的迭代过程。迭代过程基于两种众所周知的方法：混合法和外梯度法。我们得到了由这个过程产生的三个序列的一个强收敛定理。在此基础上，我们还构造了一个迭代过程来寻找两个映象的公共不动点，使得其中一个映象是非扩张的，另一个映象取自更一般的Lipschitz伪压缩映象类。
In this paper we introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on two well-known methods: hybrid and extragradient. We obtain a strong convergence theorem for three sequences generated by this process. Based on this result, we also construct an iterative process for finding a common fixed point of two mappings, such that one of these mappings is nonexpansive and the other is taken from the more general class of Lipschitz pseudocontractive mappings.