{
  "id": "2308.01003",
  "version": "v1",
  "published": "2023-08-02T08:26:13.000Z",
  "updated": "2023-08-02T08:26:13.000Z",
  "title": "Fixed point theorem for mappings contracting perimeters of triangles",
  "authors": [
    "Evgeniy Petrov"
  ],
  "comment": "8 pages, 1 figure, A full-text view-only version is available online at https://rdcu.be/dijGN",
  "journal": "J. Fixed Point Theory Appl. 25, 74 (2023)",
  "doi": "10.1007/s11784-023-01078-4",
  "categories": [
    "math.GN"
  ],
  "abstract": "We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. An example of a mapping contractive perimeters of triangles which is not a contraction mapping is constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T08:26:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "47H09"
    ],
    "keywords": [
      "mappings contracting perimeters",
      "fixed point theorem",
      "classical banach fixed-point theorem",
      "simple corollary",
      "metric spaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}