{
  "id": "2106.06495",
  "version": "v1",
  "published": "2021-06-11T16:43:43.000Z",
  "updated": "2021-06-11T16:43:43.000Z",
  "title": "Geometric properties of certain integral operators involving Hornich operations",
  "authors": [
    "S. Kumar"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "In this article, we investigate some standard geometric properties of the integral operator $$ C_{\\alpha,\\beta}[f,g](z)=\\int_{0}^{z}\\bigg(\\frac{f(w)}{w}\\bigg)^\\alpha (g'(w))^\\beta dw, \\,\\,\\, \\alpha,\\beta \\in \\mathbb{R} \\text{ and } |z|<1, $$ where $f$ and $g$ are elements of certain classical families of normalized analytic functions defined on the unit disk. Here, the exponents are chosen in such a way that the respective functions are analytic in suitable branches.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-11T16:43:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "30C45",
      "30C55"
    ],
    "keywords": [
      "integral operator",
      "hornich operations",
      "standard geometric properties",
      "normalized analytic functions",
      "unit disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}