{
  "id": "1505.04129",
  "version": "v1",
  "published": "2015-05-15T17:11:41.000Z",
  "updated": "2015-05-15T17:11:41.000Z",
  "title": "On a result of Pazy concerning the asymptotic behaviour of nonexpansive mappings",
  "authors": [
    "Heinz H. Bauschke",
    "Graeme R. Douglas",
    "Walaa M. Moursi"
  ],
  "comment": "10 pages",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "In 1971, Pazy presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping. In this note, we analyze the fixed-point free case in more detail. Our results and examples give credence to the conjecture that the iterates always converge cosmically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-15T17:11:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H09",
      "90C25"
    ],
    "keywords": [
      "asymptotic behaviour",
      "nonexpansive mapping",
      "pazy concerning",
      "fixed-point free case",
      "beautiful trichotomy result concerning"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}