{
  "id": "1501.02857",
  "version": "v1",
  "published": "2015-01-13T01:17:50.000Z",
  "updated": "2015-01-13T01:17:50.000Z",
  "title": "Characterization of generalized quasi-arithmetic means",
  "authors": [
    "Janusz Matkowski",
    "Zsolt Páles"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,\\dots,x_n):=(f_1+\\cdots+f_n)^{-1}(f_1(x_1)+\\cdots+f_n(x_n))$, where $f_1,\\dots,f_n:I\\to\\mathbb{R}$ are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic mean-type mapping induced by $M$ and a generalized bisymmetry equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-13T01:17:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B40"
    ],
    "keywords": [
      "characterization",
      "gauss composition",
      "generalized bisymmetry equation",
      "characterize generalized quasi-arithmetic means",
      "cyclic mean-type mapping"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150102857M"
    }
  }
}