{
  "id": "2202.03145",
  "version": "v1",
  "published": "2022-01-21T18:07:05.000Z",
  "updated": "2022-01-21T18:07:05.000Z",
  "title": "Jensen-type inequalities for convex and $m$-convex functions via fractional calculus",
  "authors": [
    "Yamilet Quintana",
    "José M. Rodríguez",
    "José M. Sigarreta Almira"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for $m$-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider $m=1$, we obtain new inequalities for convex functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-21T18:07:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "26A51",
      "26D15"
    ],
    "keywords": [
      "convex functions",
      "jensen-type inequalities",
      "fractional calculus",
      "boundary value problems",
      "generalized riemann-liouville-type integral operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}