{
  "id": "1910.12304",
  "version": "v1",
  "published": "2019-10-27T17:21:07.000Z",
  "updated": "2019-10-27T17:21:07.000Z",
  "title": "A New Solution to the Rhoades' Open Problem with an Application",
  "authors": [
    "Nihal Özgür",
    "Nihal Taş"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We give a new solution to the Rhoades' open problem on the discontinuity at fixed point via the notion of an $S$-metric. To do this, we inspire with the notion of a Zamfirescu mapping. Also, we consider a recent problem called the \"fixed-circle problem\" and propose a new solution to this problem as an application of our technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-27T17:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H25",
      "47H09",
      "47H10"
    ],
    "keywords": [
      "open problem",
      "application",
      "fixed-circle problem",
      "discontinuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}