{
  "id": "1802.07633",
  "version": "v1",
  "published": "2018-02-21T16:05:44.000Z",
  "updated": "2018-02-21T16:05:44.000Z",
  "title": "GÂteaux-Differentiability of Convex Functions in Infinite Dimension",
  "authors": [
    "Mohammed Bachir",
    "Adrien Fabre"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is well known that in $R^n$ , G{\\^a}teaux (hence Fr{\\'e}chet) differ-entiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point. We prove that this result extends naturally to certain infinite dimensional vector spaces, in particular to Banach spaces having a Schauder basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-21T16:05:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex functions",
      "gâteaux-differentiability",
      "infinite dimensional vector spaces",
      "schauder basis",
      "partial derivatives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}