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arXiv 2005.082512020-05-17math.FA

A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard spaces

Hadi Khatibzadeh, Hadi Pouladi

备注：: 21 pages
发表信息：: Analysis mathematica (2021)
DOI：: 10.1007/s10476-021-0080-z

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.

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