TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS
TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS
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DOI：
10.11650/tjm.16.2012.2012
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发表时间：
2012-01
影响因子：
0.4
通讯作者：
W. Takahashi;N. Wong;J. Yao
中科院分区：
文献类型：
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作者：
W. Takahashi;N. Wong;J. Yao
设C是真实的Hilbert空间H的闭凸子集.设A是C到H的逆强单调映射，B是H上的极大单调算子，使得B的定义域包含在C中.本文介绍了两种求$（A+B）^{-1 <$0 $点的迭代方案，其中$（A+B）^{-1 $> 0 $是$A+B$的零点集。然后，我们证明了Hilbert空间中的两个Halpern型强收敛定理。利用这些结果，我们得到了Hilbert空间中新的和著名的强收敛定理。
Let $C$ be a closed convex subset of a real Hilbert space $H$. Let $A$ be an inverse-strongly monotone mapping of $C$ into $H$ and let $B$ be a maximal monotone operator on $H$ such that the domain of $B$ is included in $C$. We introduce two iteration schemes of finding a point of $(A+B)^{-1}0$, where $(A+B)^{-1}0$ is the set of zero points of $A+B$. Then, we prove two strong convergence theorems of Halpern's type in a Hilbert space. Using these results, we get new and well-known strong convergence theorems in a Hilbert space.