{
  "abstract": "By a result of F. R. Keogh in 1959, we have the inequality $L(r,f)/M(r,f)\\le 2π+4\\log[(1+r)/(1-r)]$ for a starlike function $f$ on the unit disk, where $L(r,f)$ and $M(r,f)$ denote the length of the curve $θ\\mapsto f(re^{iθ})$ and the maximum value of $|f(z)|$ on the circle $|z|=r$ for $0<r<1.$ E. Crane and D. Markose in their 2005 paper showed that the constant $4$ is best possible. D. K. Thomas obtained in 1968 the inequality $L(r,f)/\\sqrt{A(r,f)}\\le 2\\sqrtπ(1+\\log[(1+r)/(1-r)])$ for a starlike function $f$, where $A(r,f)$ is the area of the image of the disk $|z|<r$ under the mapping $f.$ In this paper, we extend these results to the case of $λ$-spirallike functions for a given $λ$ with $-π/2<λ<π/2.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24035",
  "author_total": 2,
  "authors": [
    {
      "name": "Zain Shayim Alsharari"
    },
    {
      "name": "Toshiyuki Sugawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xkwesr88szaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24035",
  "fulltext_url": null,
  "id": "4xkwesr88szaz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24035",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214047176",
  "pdf_url": "https://arxiv.org/pdf/2609.24035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xkwesr88szaz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic perimeter estimates for spirallike functions",
  "title_text": "Asymptotic perimeter estimates for spirallike functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4xkwesr88szaz",
  "venue": "arXiv",
  "versions": []
}