{
  "id": "0907.2834",
  "version": "v1",
  "published": "2009-07-16T13:17:57.000Z",
  "updated": "2009-07-16T13:17:57.000Z",
  "title": "On certain classes of harmonic functions defined by the fractional derivatives",
  "authors": [
    "M. Eshaghi Gordji",
    "S. Shams",
    "A. Ebadian"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "In this paper we have introduced two new classes $\\mathcal{H}\\mathcal{M}(\\beta, \\lambda, k, \\nu)$ and $\\overline{\\mathcal{H}\\mathcal{M}} (\\beta, \\lambda, k, \\nu)$ of complex valued harmonic multivalent functions of the form $f = h + \\overline g$, satisfying the condition \\[ Re \\{(1 - \\lambda) \\frac{\\Omega^vf}{z} + \\lambda(1-k) \\frac{(\\Omega^vf)'}{z'} + \\lambda k \\frac{(\\Omega^vf)''}{z''} \\} > \\beta, (z\\in \\mathcal{D})\\] where $h$ and $g$ are analytic in the unit disk $\\mathcal{D} = \\{z : |z| < 1\\}.$ A sufficient coefficient condition for this function in the class $\\mathcal{H}\\mathcal{M}(\\beta, \\lambda, k, \\nu)$ and a necessary and sufficient coefficient condition for the function $f$ in the class $\\overline{\\mathcal{H}\\mathcal{M}}(\\beta, \\lambda, k, \\nu)$ are determined. We investigate inclusion relations, distortion theorem, extreme points, convex combination and other interesting properties for these families of harmonic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-16T13:17:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C45",
      "30C80"
    ],
    "keywords": [
      "harmonic functions",
      "fractional derivatives",
      "sufficient coefficient condition",
      "complex valued harmonic multivalent functions",
      "distortion theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2834E"
    }
  }
}