{
  "abstract": "We introduce asymptotically Hölder nonexpansive mappings and mappings of asymptotically Hölder nonexpansive type, in which the Hölder exponents converge to one along the iterates. We prove that if \\(K\\) is a nonempty closed bounded convex subset of a Banach space \\(X\\) with characteristic of convexity \\(ε_0(X)<1\\), then every self-mapping of \\(K\\) of asymptotically Hölder nonexpansive type admits a point \\(x\\in K\\) such that \\(T^n x\\to x\\). Consequently, a fixed point exists whenever some positive iterate of \\(T\\) is continuous; in particular, this applies to asymptotically Hölder nonexpansive mappings. We also obtain fixed-point-free constructions in spaces containing copies of \\(c_0\\), and a related construction on a bounded convex, not necessarily closed, subset of every Banach space containing an isomorphic copy of \\(\\ell_1\\). Further examples show that the new classes properly extend their classical counterparts and may contain mappings with no continuous positive iterate. Finally, we examine Lin's renorming of \\(\\ell_1\\), identify an obstruction related to shift-type constructions, and establish a shrinking-diagonal criterion that reduces the remaining closed-set problem to the construction of a suitably controlled uniformly Lipschitzian mapping.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30678",
  "author_total": 2,
  "authors": [
    {
      "name": "Cleon S. Barroso"
    },
    {
      "name": "Carlos Sérgio R. da Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hmp0a5pqma0z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30678",
  "fulltext_url": null,
  "id": "6hmp0a5pqma0z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30678",
  "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.FA"
    ],
    [
      "openalex",
      "2608|Fixed Point Theorems Analysis"
    ]
  ],
  "openalex": "W7163006334",
  "pdf_url": "https://arxiv.org/pdf/2605.30678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hmp0a5pqma0z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2605.30678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fixed point results for mappings of asymptotically Hölder nonexpansive type",
  "title_text": "Fixed point results for mappings of asymptotically Hölder nonexpansive type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/6hmp0a5pqma0z",
  "venue": "arXiv",
  "versions": []
}