{
  "id": "2009.01688",
  "version": "v1",
  "published": "2020-09-01T06:06:15.000Z",
  "updated": "2020-09-01T06:06:15.000Z",
  "title": "New Refinements of Cusa-Huygens inequality",
  "authors": [
    "Christophe Chesneau",
    "Marko Kostic",
    "Branko Malesevic",
    "Bojan Banjac",
    "Yogesh J. Bagul"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In the paper, we refine and extend Cusa-Huygens inequality by simple functions. In particular, we determine sharp bounds for $\\sin(x) /x$ of the form $(2+\\cos(x))/3 -(2/3-2/\\pi)\\Upsilon(x)$, where $\\Upsilon(x) >0$ for $x\\in (0, \\pi/2)$, $\\Upsilon(0)=0$ and $\\Upsilon(\\pi/2)=1$, such that $\\sin x/x$ and the proposed bounds coincide at $x=0$ and $x=\\pi/2$. The hierarchy of the obtained bounds is discussed, along with graphical study. Also, alternative proofs of the main result are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-01T06:06:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "refinements",
      "determine sharp bounds",
      "extend cusa-huygens inequality",
      "simple functions",
      "bounds coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}