{
  "id": "2211.16026",
  "version": "v1",
  "published": "2022-11-29T08:50:12.000Z",
  "updated": "2022-11-29T08:50:12.000Z",
  "title": "A variation of continuity in $n$-normed spaces",
  "authors": [
    "Sibel Ersan"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The s-th forward difference sequence that tends to zero, inspired by the consecutive terms of a sequence approaching zero, is examined in this study. Functions that take sequences satisfying this condition to sequences satisfying the same condition are called s-ward continuous. Inclusion theorems that are related to this kind of uniform continuity and continuity are also considered. Additionally, the concept of $s$-ward compactness of a subset of $X$ via $s$-quasi-Cauchy sequences are investigated. One finds out that the uniform limit of any sequence of $s$-ward continuous function is $s$-ward continuous and the set of $s$-ward continuous functions is a closed subset of the set of continuous functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-29T08:50:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normed spaces",
      "ward continuous function",
      "s-th forward difference sequence",
      "inclusion theorems",
      "uniform continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}