%0 Journal Article
%T Non-linear ergodic theorems in complete non-positive curvature metric spaces
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Ahmadi Kakavandi, B.
%A Amini, M.
%D 2011
%\ 09/15/2011
%V 37
%N No. 3
%P 11-20
%! Non-linear ergodic theorems in complete non-positive curvature metric spaces
%K Hadamard Space
%K continuous non-expansive semigroup
%K invariant mean
%K asymptotic center
%K non-linear ergodic theorem
%R
%X 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.
%U http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdf