{
  "id": "2303.10206",
  "version": "v1",
  "published": "2023-03-17T18:57:41.000Z",
  "updated": "2023-03-17T18:57:41.000Z",
  "title": "Non-stationary $α$-fractal functions and their dimensions in various function spaces",
  "authors": [
    "Anarul Islam Mondal",
    "Sangita Jha"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article, we study the novel concept of non-stationary iterated function systems (IFSs) introduced by Massopust in 2019. At first, using a sequence of different contractive operators, we construct non-stationary $\\alpha$-fractal functions on the space of all continuous functions. Next, we provide some elementary properties of the fractal operator associated with the nonstationary $\\alpha$-fractal functions. Further, we show that the proposed interpolant generalizes the existing stationary interpolant in the sense of IFS. For a class of functions defined on an interval, we derive conditions on the IFS parameters so that the corresponding non-stationary $\\alpha$-fractal functions are elements of some standard spaces like bounded variation space, convex Lipschitz space, and other function spaces. Finally, we discuss the dimensional analysis of the corresponding non-stationary $\\alpha$-fractal functions on these spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-17T18:57:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "26A18",
      "35B41",
      "41A30",
      "46B70"
    ],
    "keywords": [
      "fractal functions",
      "function spaces",
      "dimensions",
      "non-stationary iterated function systems",
      "corresponding non-stationary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}