{
  "id": "2003.12714",
  "version": "v1",
  "published": "2020-03-28T05:24:01.000Z",
  "updated": "2020-03-28T05:24:01.000Z",
  "title": "Some inequalities on $h$-convex functions",
  "authors": [
    "M. Abbasi",
    "A. Morassaei",
    "F. Mirzapour"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we state some characterizations of $h$-convex function is defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for $h$-convex function. We will also define $h$-convex function for operators on a Hilbert space and present the operator version of the Jensen-Mercer inequality. Lastly, we propound the complementary inequality of Jensen's inequality for $h$-convex functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-28T05:24:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex function",
      "jensen-mercer inequality",
      "jensens inequality",
      "linear space",
      "convex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}