{
  "id": "1309.1772",
  "version": "v3",
  "published": "2013-09-06T20:29:45.000Z",
  "updated": "2016-07-30T12:35:25.000Z",
  "title": "Notes on the differentiation of quasi-convex functions",
  "authors": [
    "F. Reese Harvey",
    "H. Blaine Lawson Jr"
  ],
  "comment": "An appendix has been added discussing the Hiriart-Urruty and Plazanet characterization of C^{1,1} in terms of quasi-convexity",
  "categories": [
    "math.AP",
    "math.CA",
    "math.CV",
    "math.DG"
  ],
  "abstract": "This expository paper presents elementary proofs of four basic results concerning derivatives of quasi-convex functions. They are combined into a fifth theorem which is simple to apply and adequate in many cases. Along the way we establish the equivalence of the basic lemmas of Jensen and Slodkowski.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-02T16:15:13.000Z",
      "comment": "Typographical errors corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-07-30T12:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D40",
      "52A41"
    ],
    "keywords": [
      "quasi-convex functions",
      "differentiation",
      "basic results concerning derivatives",
      "basic lemmas",
      "expository paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1772R"
    }
  }
}