{
  "id": "1902.09284",
  "version": "v1",
  "published": "2019-02-25T14:24:01.000Z",
  "updated": "2019-02-25T14:24:01.000Z",
  "title": "A new metastable convergence criterion and an application in the theory of uniformly convex Banach spaces",
  "authors": [
    "Thomas Powell"
  ],
  "categories": [
    "math.FA",
    "math.LO"
  ],
  "abstract": "We study a convergence criterion which generalises the notion of being monotonically decreasing, and introduce a quantitative version of this criterion, a so called metastable rate of asymptotic decreasingness. We then present a concrete application in the fixed point theory of uniformly convex Banach spaces, in which we carry out a quantitative analysis of a convergence proof of Kirk and Sims. More precisely, we produce a rate of metastability (in the sense of Tao) for the Picard iterates of mappings T which satisfy a variant of the convergence criterion, and whose fixed point set has nonempty interior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-25T14:24:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniformly convex banach spaces",
      "metastable convergence criterion",
      "application",
      "fixed point set",
      "picard iterates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}