{
  "abstract": "The classical Banach principle relies on contractive sequences being Cauchy. Gregori and Sapena (2002) established a fuzzy analogue but required this as an extra hypothesis, leaving it as an open problem. Gregori et al. (2020) later asked whether strictly fuzzy $ψ$-contractive sequences are necessarily Cauchy. We settle both problems negatively via a single counterexample: in a constructed GV-fuzzy metric space, there exists a sequence which is both GS-contractive and strictly fuzzy $ψ$-contractive, yet not Cauchy. This shows that contractivity never implies Cauchyness in general GV-fuzzy metric spaces, and additional structural conditions in fuzzy fixed point theorems are indispensable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03372",
  "author_total": 3,
  "authors": [
    {
      "name": "Fengshuo Xu"
    },
    {
      "name": "Haitao Ji"
    },
    {
      "name": "Dong Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pk2xynr625px.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03372",
  "fulltext_url": null,
  "id": "4pk2xynr625px",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03372",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2608|Fixed Point Theorems Analysis"
    ]
  ],
  "openalex": "W7208758430",
  "pdf_url": "https://arxiv.org/pdf/2609.03372",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pk2xynr625px.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03372",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03372"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On fuzzy contractions in fuzzy metric spaces",
  "title_text": "On fuzzy contractions in fuzzy metric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/4pk2xynr625px",
  "venue": "arXiv",
  "versions": []
}