@article {
author = {Ahmadi Kakavandi, B. and Amini, M.},
title = {Non-linear ergodic theorems in complete non-positive curvature metric spaces},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {37},
number = {No. 3},
pages = {11-20},
year = {2011},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Hadamard spaces, which include for example (possibly infinite-dimensional) complete simply connected Riemannian manifolds with non-positive sectional curvature.},
keywords = {Hadamard Space,continuous non-expansive semigroup,invariant mean,asymptotic center,non-linear ergodic theorem},
url = {http://bims.iranjournals.ir/article_348.html},
eprint = {http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdf}
}