{
  "id": "1709.08611",
  "version": "v1",
  "published": "2017-09-25T17:41:23.000Z",
  "updated": "2017-09-25T17:41:23.000Z",
  "title": "A Characterization of Convex Functions",
  "authors": [
    "Paolo Leonetti"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\\to \\mathbf{R}\\cup \\{+\\infty\\}$ is convex if and only if for all $x,y \\in D$ there exists $\\alpha=\\alpha(x,y) \\in (0,1)$ such that $f(\\alpha x+(1-\\alpha)y) \\le \\alpha f(x)+(1-\\alpha)f(y)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-25T17:41:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "25B62",
      "26A51",
      "52A07"
    ],
    "keywords": [
      "convex functions",
      "characterization",
      "real vector space",
      "convex subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}