{
  "id": "1307.0638",
  "version": "v1",
  "published": "2013-07-02T09:19:40.000Z",
  "updated": "2013-07-02T09:19:40.000Z",
  "title": "Hyers--Ulam stability of derivations and linear functions",
  "authors": [
    "Zoltán Boros",
    "Eszter Gselmann"
  ],
  "comment": "9 pages; published in Aequationes Mathematicae in 2010",
  "doi": "10.1007/s00010-010-0026-1",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, then $f$ can be represented as the sum of a derivation and a linear function. When, instead of the additivity of $f$, it is assumed that, in addition, the Cauchy difference of $f$ is bounded, a stability theorem is obtained for such characterizations of derivations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-02T09:19:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B82",
      "39B72"
    ],
    "keywords": [
      "linear function",
      "hyers-ulam stability",
      "basic algebraic curves",
      "additive real function",
      "derivation rule"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0638B"
    }
  }
}