{
  "id": "2003.10892",
  "version": "v1",
  "published": "2020-03-24T14:43:50.000Z",
  "updated": "2020-03-24T14:43:50.000Z",
  "title": "A new treatment of convex functions",
  "authors": [
    "M. Sababheh",
    "S. Furuichi",
    "H. R. Moradi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In particular, we define what we called $g-$convexity as a generalization of $\\log-$convexity. Then we prove that $g-$convex functions have better estimates in certain known inequalities like the Hermite-Hadard inequality, super additivity of convex functions, the Majorization inequality and some means inequalities. Strongly related to this, we define the index of convexity as a measure of ``how much the function is convex\". Applications including Hilbert space operators, matrices and entropies will be presented in the end.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-24T14:43:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex functions",
      "better estimates",
      "hilbert space operators",
      "super additivity",
      "major role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}