{
  "id": "1109.1773",
  "version": "v1",
  "published": "2011-09-08T17:07:28.000Z",
  "updated": "2011-09-08T17:07:28.000Z",
  "title": "Characterization of a generalized triangle inequality in normed spaces",
  "authors": [
    "F. Dadipour",
    "M. S. Moslehian",
    "J. M. Rassias",
    "S. -E. Takahasi"
  ],
  "comment": "11 Pages, to appear in Nonlinear Anal-TMA",
  "journal": "Nonlinear Anal-TMA 75 (2012), no. 2, 735-741",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "For a normed linear space $(X,|\\cdot|)$ and $p>0$ we characterize all $n$-tuples $(\\mu_1,...,\\mu_n)\\in\\mathbb{R}^{n}$ for which the generalized triangle inequality of the second type $$\\|x_1+...+x_n\\|^p\\leq\\frac{|x_1|^p}{\\mu_1}+...+\\frac{|x_n|^p}{\\mu_n}$$ holds for any $x_1,...,x_n\\in X$. We also characterize $(\\mu_1,...,\\mu_n)\\in\\mathbb{R}^{n}$ for which the reverse of the inequality above holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-08T17:07:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C15",
      "46B20",
      "46C05"
    ],
    "keywords": [
      "generalized triangle inequality",
      "normed spaces",
      "characterization",
      "normed linear space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1773D"
    }
  }
}