{
  "abstract": "We determine the radii of concavity for the classes $\\mathcal{S}_e^*$ and $\\mathcal{C}_e$ of univalent functions associated with the exponential mapping $e^z$. Under the geometric framework of Avkhadiev--Wirths for conformal mappings with unbounded convex complements of opening angle $πA$ ($A \\in (1,2]$), the radii are characterized by explicit transcendental equations. Sharpness is established globally by constructing explicit univalent extremal functions related to the disk automorphism $ω_0(z) = -z$, and the strict monotonicity of these radii with respect to the parameter $A$ is verified numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26154",
  "author_total": 2,
  "authors": [
    {
      "name": "Pradip Das"
    },
    {
      "name": "Nabadwip Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6w8na960gvg6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26154",
  "fulltext_url": null,
  "id": "6w8na960gvg6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26154",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214078440",
  "pdf_url": "https://arxiv.org/pdf/2609.26154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6w8na960gvg6w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26154"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping",
  "title_text": "Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6w8na960gvg6w",
  "venue": "arXiv",
  "versions": []
}