A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard spaces
Functional Analysis
2021-05-07 v1
Abstract
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.
Cite
@article{arxiv.2005.08251,
title = {A Mean Ergodic Theorem for Nonexpansive Mappings in Hadamard spaces},
author = {Hadi Khatibzadeh and Hadi Pouladi},
journal= {arXiv preprint arXiv:2005.08251},
year = {2021}
}
Comments
21 pages