{
  "id": "2103.13914",
  "version": "v1",
  "published": "2021-03-25T15:25:01.000Z",
  "updated": "2021-03-25T15:25:01.000Z",
  "title": "Fixed Point Theorems in M-distance Spaces",
  "authors": [
    "Vladyslav Babenko",
    "Vira Babenko",
    "Oleg Kovalenko"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including metric and uniform spaces. On the other hand, compared to the so-called cone metric spaces and $K$-metric spaces, we do not require that the distance function range has a linear structure. We also consider several applications of the obtained fixed point theorems. In particular, we consider the questions of the existence of solutions of the Fredholm integral equation in $L$-spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T15:25:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "47H09"
    ],
    "keywords": [
      "fixed point theorems",
      "m-distance spaces",
      "fredholm integral equation",
      "cone metric spaces",
      "distance function range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}