{
  "abstract": "A normalized analytic function $f(z)=z+\\sum_{k=n+1}^{\\infty}a_kz^k$ defined on the unit disk $\\mathbb{D}$ is called Ma--Minda starlike or Ma--Minda convex if $zf'(z)/f(z)$ or $1+zf''(z)/f'(z)$, respectively, is subordinate to a Ma--Minda function $φ$. In this paper, we investigate the radii of Ma--Minda starlikeness and convexity for functions satisfying $|f''(z)|<M$ in $\\mathbb{D}$. We first develop a unified approach for determining these radii and then apply it to obtain explicit radius estimates for several important choices of the Ma--Minda function~$φ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07845",
  "author_total": 2,
  "authors": [
    {
      "name": "Poomalai Palanisamy"
    },
    {
      "name": "Ravichandran Vaithiyanathan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48rzj52nqjv9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07845",
  "fulltext_url": null,
  "id": "48rzj52nqjv9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07845",
  "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": "W7220967808",
  "pdf_url": "https://arxiv.org/pdf/2610.07845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48rzj52nqjv9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.07845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07845"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Radius of Ma-Minda Starlikeness and Convexity for Functions with Bounded Second Derivative",
  "title_text": "Radius of Ma-Minda Starlikeness and Convexity for Functions with Bounded Second Derivative",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/48rzj52nqjv9g",
  "venue": "arXiv",
  "versions": []
}