{
  "id": "1408.2250",
  "version": "v1",
  "published": "2014-08-10T16:11:48.000Z",
  "updated": "2014-08-10T16:11:48.000Z",
  "title": "Sharp Cusa type inequalities for trigonometric functions with two parameters",
  "authors": [
    "Zhen-Hang Yang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\left( p,q\\right) \\mapsto \\beta \\left( p,q\\right) $ be a function defined on $\\mathbb{R}^{2}$. We determine the best or better $p,q$ such that the inequality% \\begin{equation*} \\left( \\frac{\\sin x}{x}\\right) ^{p}<\\left( >\\right) 1-\\beta \\left( p,q\\right) +\\beta \\left( p,q\\right) \\cos ^{q}x \\end{equation*}% holds for $x\\in \\left( 0,\\pi /2\\right) $, and obtain a lot of new and sharp Cusa type inequalities for trigonometric functions. As applications, some new Shafer-Fink type and Carlson type inequalities for arc sine and arc cosine functions, and new inequalities for trigonometric means are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-10T16:11:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D05",
      "33B10",
      "26A48",
      "26D15"
    ],
    "keywords": [
      "sharp cusa type inequalities",
      "trigonometric functions",
      "parameters",
      "carlson type inequalities",
      "arc cosine functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2250Y"
    }
  }
}