A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings
A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings
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DOI：
10.1155/2007/64874
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发表时间：
2007-05
影响因子：
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通讯作者：
H. Zhou;Y. Cho;SM Kang
中科院分区：
文献类型：
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作者：
H. Zhou;Y. Cho;SM Kang
假设 是实均匀凸且光滑的 Banach 空间的非空闭凸子集，具有阳光非膨胀回缩。令 为 分别关于序列 、 的两个弱向内且渐近非扩张映射。假设 是由 、 、 对于所有 迭代生成的序列，其中 、 、 和 是对于某些满足条件 的三个实数序列。然后，我们有以下内容。 (1) 如果 和 之一是完全连续的或半紧的 和 ，则 到 some 的强收敛成立。 (2) 若 是实一致凸Banach 空间，满足Opial 条件或其范数为Fréchet 可微，则证明对some 的弱收敛性。
Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicompact and , then the strong convergence of to some is established. (2) If is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Fréchet differentiable, then the weak convergence of to some is proved.