{
  "id": "1310.6698",
  "version": "v1",
  "published": "2013-10-23T06:52:54.000Z",
  "updated": "2013-10-23T06:52:54.000Z",
  "title": "Some Monotonicity Properties of Convex Functions with Applications",
  "authors": [
    "Jamal Rooin",
    "Hossein Dehghan"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\\frac{b-a}{n+1}\\sum_{i=0}^n f\\left(a+i\\frac{b-a}{n}\\right)$ is decreasing while $\\frac{b-a}{n-1}\\sum_{i=1}^{n-1} f\\left(a+i\\frac{b-a}{n}\\right)$ is an increasing sequence. These give us a new refinement of the Hermitt-Hadamard inequality. Moreover, we give a refinement of the classical Alzer's inequality together with a suitable converse to it. Applications regarding to some important convex functions are also included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-23T06:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "26A51",
      "26A06"
    ],
    "keywords": [
      "monotonicity property",
      "applications",
      "special riemann sums",
      "important convex functions",
      "classical alzers inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6698R"
    }
  }
}