{
  "id": "1804.03651",
  "version": "v1",
  "published": "2018-04-10T17:53:54.000Z",
  "updated": "2018-04-10T17:53:54.000Z",
  "title": "Structure for $g$-Metric Spaces and Related Fixed Point Theorems",
  "authors": [
    "Hayoung Choi",
    "Sejong Kim",
    "Seung Yeop Yang"
  ],
  "comment": "41 pages, 2 figures",
  "journal": "Kyungpook Mathematical Journal, (2022), 62(4), 773-785",
  "doi": "10.5666/KMJ.2022.62.4.773",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we propose a generalized notion of a distance function, called a $g$-metric. The $g$-metric with degree $n$ is a distance of $n+1$ points, generalizing the ordinary distance between two points and $G$-metric between three points. Indeed, it is shown that the $g$-metric with degree 1 (resp. degree 2) is equivalent to the ordinary metric (resp. the $G$-metric). Fundamental properties and several examples for the $g$-metric are also given. Moreover, topological properties on the $g$-metric space including the convergence of sequences and the continuity of mappings on the $g$-metric space are studied. Finally, we generalize some well-known fixed point theorems including Banach contraction mapping principle and \\'Ciri\\'c fixed point theorem in the $g$-metric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-10T17:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54H25",
      "37C25",
      "54E99"
    ],
    "keywords": [
      "related fixed point theorems",
      "metric space",
      "ciric fixed point theorem",
      "banach contraction mapping principle",
      "well-known fixed point theorems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}