{
  "id": "1405.6637",
  "version": "v2",
  "published": "2014-05-26T16:44:51.000Z",
  "updated": "2014-07-24T17:27:26.000Z",
  "title": "The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces",
  "authors": [
    "Miroslav Bacak",
    "Simeon Reich"
  ],
  "comment": "Accepted in JFPTA",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study a nonlinear semigroup associated to a nonexpansive mapping on a Hadamard space and establish its weak convergence to a fixed point. A discrete-time counterpart of such a semigroup, the proximal point algorithm, turns out to have the same asymptotic behavior. This complements several results in the literature -- both classical and more recent ones. As an application, we obtain a new approach to heat flows in singular spaces for discrete, as well as continuous times.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-24T17:27:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H20",
      "60J45"
    ],
    "keywords": [
      "asymptotic behavior",
      "hadamard space",
      "proximal point algorithm",
      "discrete-time counterpart",
      "singular spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6637B"
    }
  }
}