{
  "id": "2001.08158",
  "version": "v1",
  "published": "2020-01-22T17:28:53.000Z",
  "updated": "2020-01-22T17:28:53.000Z",
  "title": "Fixed point properties for semigroups of nonlinear mappings on unbounded sets",
  "authors": [
    "Anthony T. -M. Lau",
    "Yong Zhang"
  ],
  "comment": "22 pages",
  "journal": "Journal of Mathematical Analysis and Applications 433 (2016), 1204-1219",
  "categories": [
    "math.FA"
  ],
  "abstract": "A well-known result of W. Ray asserts that if $C$ is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping $T$: $C\\to C$ that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup $S$ of nonexpansive mappings acting on a closed convex subset $C$ of a Hilbert space, assuming that there is a point $c\\in C$ with a bounded orbit and assuming that certain subspace of $C_b(S)$ has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 \\cite{Neu} and formalized by Day in 1957 \\cite{Day}. In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-22T17:28:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "47H09",
      "43A07",
      "20M30",
      "47H20"
    ],
    "keywords": [
      "nonlinear mappings",
      "unbounded sets",
      "left invariant mean",
      "hilbert space",
      "common fixed point properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}