An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space
An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space
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希尔伯特空间中非扩张映射半群的遍历定理
DOI：
10.1016/0022-247x(82)90032-4
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发表时间：
1982
影响因子：
1.3
通讯作者：
G. Rodé
中科院分区：
文献类型：
--
作者：
G. Rodé
[摘要]JB . Baillon [CR]；巴黎爵士。a . 280(1975)， 1511-1514]证明了Hilbert空间中单个非扩张映射的遍历定理，这是von Neumann平均遍历定理的非线性版本。本文研究了一类非扩张映射半群的遍历性。我们试图找到半群上的均值序列，推广N上的Cesàro均值，使得相应的非扩张映射序列收敛到公共不动点集合上的投影。我们的证明方法是A. Pazy对bailon定理的证明[Israel J. Math. 26(1977)， 197-204]的适当修改。
Abstract JB Baillon [CR Acad. Sci. Paris Ser. A. 280 (1975), 1511–1514] proved an ergodic theorem for a single nonexpansive mapping in a Hilbert space, which is a nonlinear version of von Neumann's mean ergodic theorem. In this paper, we study the ergodic behavior of a semigroup of nonexpansive mappings. We try to find a sequence of means on the semigroup, generalizing the Cesàro means on N, such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed-points. Our method of proof is an appropriate modification of A. Pazy's proof [Israel J. Math. 26 (1977), 197–204] of Baillon's theorem.