{
  "id": "1402.3357",
  "version": "v1",
  "published": "2014-02-14T04:23:55.000Z",
  "updated": "2014-02-14T04:23:55.000Z",
  "title": "Parameter convexity and concavity of generalized trigonometric functions",
  "authors": [
    "D. B. Karp",
    "E. G. Prilepkina"
  ],
  "comment": "15 pages, no figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the convexity properties of the generalized trigonometric functions considered as functions of parameter. We show that $p\\to\\sin_p(y)$ and $p\\to\\cos_p(y)$ are log-concave on the appropriate intervals while $p\\to\\tan_p(y)$ is log-convex. We also prove similar facts about the generalized hyperbolic functions. In particular, our results settle the major part of a conjecture put forward in a recent paper by Baricz, Bhayo and Vuorinen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-14T04:23:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B99",
      "33E30"
    ],
    "keywords": [
      "generalized trigonometric functions",
      "parameter convexity",
      "convexity properties",
      "appropriate intervals",
      "similar facts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.3357K"
    }
  }
}