{
  "id": "1501.06187",
  "version": "v1",
  "published": "2015-01-25T17:35:31.000Z",
  "updated": "2015-01-25T17:35:31.000Z",
  "title": "Qualitative approximation of solutions to difference equations",
  "authors": [
    "Janusz Migda"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We present a new approach to the theory of asymptotic properties of solutions of difference equations. Usually, two sequences $x,y$ are called asymptotically equivalent if the sequence $x-y$ is convergent to zero i.e., $x-y\\in c_0$, where $c_0$ denotes the space of all convergent to zero sequences. We replace the space $c_0$ by various subspaces of $c_0$. Our approach is based on using the iterated remainder operator. Moreover, we use the regional topology on the space of all real sequences and the `regional' version of the Schauder fixed point theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-25T17:35:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39A10"
    ],
    "keywords": [
      "difference equations",
      "qualitative approximation",
      "schauder fixed point theorem",
      "convergent",
      "zero sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150106187M"
    }
  }
}