{
  "abstract": "In this article, we investigate refined and generalized versions of the Bohr and Bohr--Rogosinski inequalities for a normalized subclass $\\mathcal{P}_{\\mathcal{H}}^{0}(α)$ ($0 \\le α< 1$) of univalent close-to-convex harmonic mappings $f = h + \\overline{g}$ defined on the open unit disk $\\mathbb{D} \\subset \\mathbb{C}$. By incorporating non-negative monotone increasing functions associated with the planar area integral $S_r/π$ of the image domain $f(\\mathbb{D}_r)$, we establish new sharp Bohr-type inequalities expressed in terms of the Euclidean distance $d(f(0), \\partial f(\\mathbb{D}))$. Furthermore, we establish sharp Bohr--Rogosinski-type inequalities involving powers of the modulus of the mapping $|f(z)|^p$ ($p \\ge 1$). All associated radii are proven to be sharp, and extremal functions realizing the equality cases are explicitly identified. As applications, our results generalize and unify several well-known classical and recent theorems in geometric function theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08600",
  "author_total": 2,
  "authors": [
    {
      "name": "Molla Basir Ahamed"
    },
    {
      "name": "Partha Pratim Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pretsedh3a1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08600",
  "fulltext_url": null,
  "id": "3pretsedh3a1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08600",
  "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": "W7211994911",
  "pdf_url": "https://arxiv.org/pdf/2609.08600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pretsedh3a1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Bohr and Bohr-Rogosinski inequalities involving area measure for close-to-convex harmonic mappings",
  "title_text": "Sharp Bohr and Bohr-Rogosinski inequalities involving area measure for close-to-convex harmonic mappings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3pretsedh3a1g",
  "venue": "arXiv",
  "versions": []
}