Hadamard空间中非扩张映象的平均遍历定理
A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard spaces
摘要：
本文证明了Hadamard（非正曲率度量）空间中非扩张映象的一个平均遍历定理，推广了Baillon非线性遍历定理.主要结果表明，具有非空不动点集的非扩张映射的Karcher迭代平均序列弱收敛于该映射的一个不动点。这一结果对1-参数连续压缩半群也成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
