论文标题
Hadamard空间中非专用映射的平均千古定理
A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard spaces
论文作者
论文摘要
在本文中，我们证明了Hadamard（非阳性曲率度量）空间中非专用映射的平均段定理，该空间扩展了Baillon非线性ergodic定理。主要结果表明，具有非空置固定点集的非跨度映射的Karcher给出的序列弱收敛到映射的固定点。对于1参数连续的收缩半群也是如此。
In this paper, we prove a mean ergodic theorem for nonexpansive mappings in Hadamard (nonpositive curvature metric) spaces, which extends the Baillon nonlinear ergodic theorem. The main result shows that the sequence given by the Karcher means of iterations of a nonexpansive mapping with a nonempty fixed point set converges weakly to a fixed point of the mapping. This result also remains true for a 1-parameter continuous semigroup of contractions.
