{
  "id": "1502.02250",
  "version": "v1",
  "published": "2015-02-08T13:47:21.000Z",
  "updated": "2015-02-08T13:47:21.000Z",
  "title": "Characterizing of Inner Product Spaces by the Mapping $n_{x,y}$",
  "authors": [
    "Hossein Dehghan"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "For the vectors $x$ and $y$ in a normed linear spaces $X$, the mapping $n_{x,y}: \\mathbb{R}\\to \\mathbb{R}$ is defined by $n_{x,y}(t)=\\|x+ty\\|$. In this note, comparing the mappings $n_{x,y}$ and $n_{y,x}$ we obtain a simple and useful characterization of inner product spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-08T13:47:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inner product spaces",
      "characterizing",
      "normed linear spaces",
      "useful characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}