{
  "id": "2405.11648",
  "version": "v1",
  "published": "2024-05-19T18:58:35.000Z",
  "updated": "2024-05-19T18:58:35.000Z",
  "title": "New directions in fixed point theory in $G$-metric spaces and applications to mappings contracting perimeters of triangles",
  "authors": [
    "Mohamed Jleli",
    "Cristina Maria Pacurar",
    "Bessem Samet"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We are concerned with the study of fixed points for mappings $T: X\\to X$, where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006) 289--297] by Mustafa and Sims, a great interest was devoted to the study of fixed points in $G$-metric spaces. In 2012, the first and third authors observed that several fixed point theorems established in $G$-metric spaces are immediate consequences of known fixed point theorems in standard metric spaces. This observation demotivated the investigation of fixed points in $G$-metric spaces. In this paper, we open new directions in fixed point theory in $G$-metric spaces. Namely, we establish new versions of the Banach, Kannan and Reich fixed point theorems in $G$-metric spaces. We point out that the approach used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1--7] is inapplicable in the present study. We also provide some interesting applications related to mappings contracting perimeters of triangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-19T18:58:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54E50",
      "47S20"
    ],
    "keywords": [
      "mappings contracting perimeters",
      "applications",
      "directions",
      "third authors",
      "fixed point theory appl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}