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 -