TY - JOUR
ID - 348
TI - Non-linear ergodic theorems in complete non-positive curvature metric spaces
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Ahmadi Kakavandi, B.
AU - Amini, M.
AD - Tarbiat Modares University
Y1 - 2011
PY - 2011
VL - 37
IS - No. 3
SP - 11
EP - 20
KW - Hadamard Space
KW - continuous non-expansive semigroup
KW - invariant mean
KW - asymptotic center
KW - non-linear ergodic theorem
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_348.html
L1 - http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdf
ER -