{
  "id": "1604.03358",
  "version": "v1",
  "published": "2016-04-12T12:01:36.000Z",
  "updated": "2016-04-12T12:01:36.000Z",
  "title": "New Hermite-Hadamard Type Inequalities for Twice Differentiable Composite $(h-s)_2$-Convex Functions",
  "authors": [
    "Peter Olamide Olanipekun",
    "Adesanmi Alao Mogbademu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In a recent paper [9], Ozdemir, Tunc and Akdemir defined two new classes of convex functions with which they proved some Hermite-Hadamard type inequalities. As an Open problem, they asked for conditions under which the composition of two functions belong to their newly defined class of convex functions and if Hermite-Hadamard type inequalities can be obtained. In this paper, we respond to the Open problems and prove some new Hermite-Hadamard inequalities for twice differentiable composition whose second derivative is $((h-s)_{2}, I)$-convex. Our results are applied to some special means of real numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T12:01:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "26A51",
      "26E70"
    ],
    "keywords": [
      "hermite-hadamard type inequalities",
      "convex functions",
      "twice differentiable composite",
      "open problem",
      "real numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160403358O"
    }
  }
}