{
  "id": "2101.10770",
  "version": "v1",
  "published": "2021-01-26T13:25:24.000Z",
  "updated": "2021-01-26T13:25:24.000Z",
  "title": "New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces",
  "authors": [
    "Nabil Mlaiki",
    "Nihal Ozgur",
    "Nihal Tas"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.GN"
  ],
  "abstract": "The fixed-circle problem is a recent problem about the study of geometric properties of the fixed point set of a self-mapping on metric (resp. generalized metric) spaces. The fixed-disc problem occurs as a natural consequence of this problem. Our aim in this paper, is to investigate new classes of self-mappings which satisfy new specific type of contraction on a metric space. We see that the fixed point set of any member of these classes contains a circle (or a disc) called the fixed circle (resp. fixed disc) of the corresponding self-mapping. For this purpose, we introduce the notions of an $F_{c}$-contractive mapping and an $F_{c}$-expanding mapping. Activation functions with fixed circles (resp. fixed discs) are often seen in the study of neural networks. This shows the effectiveness of our fixed-circle (resp. fixed-disc) results. In this context, our theoretical results contribute to future studies on neural networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-26T13:25:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54H25"
    ],
    "keywords": [
      "metric space",
      "fixed-circle results",
      "fc-expanding mappings",
      "fixed point set",
      "neural networks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}