{
  "abstract": "Let $\\mathbb{B}$ be the unit ball in a complex Banach space ${\\mathbb X}$. We study biholomorphic mappings $F: \\mathbb{B} \\to {\\mathbb X}$ of the form $F(z) = f(z)z$ for $z \\in \\mathbb{B}$, where $f: \\mathbb{B} \\to \\mathbb{C}$ is a holomorphic function satisfying $f(0) = 1$. Our main contributions are as follows: Inclusion Results: We establish inclusion conditions for $\\mathcal{M}_α(\\mathbb{B})$, class of $α$-convex functions in $\\mathbb{B}$ to belong to the classes of starlike mappings or quasi-convex mappings of type $B$ on $\\mathbb{B}$ for specified ranges of $α$. Characterization: We prove that $F(z) = \\frac{f(l_{u}(z))}{l_{u}(z)}z \\in \\mathcal{M}_α(\\mathbb{B})$ if and only if $f \\in \\mathcal{M}_α(\\mathbb{U})$, where $f \\in \\mathcal{S}(\\mathbb{U})$, $u \\in {\\mathbb X}$ with $\\|u\\| = 1$, and $l_{u} \\in T(u)$. Duality: We present a duality relationship between the classes $\\mathcal{S}^*(\\mathbb{U})$ and $\\mathcal{M}_α(\\mathbb{B})$ for $α\\ge 0$. Hankel Determinant Bounds: We determine sharp upper bounds for the second Hankel determinant of mappings in $\\mathcal{M}_α(\\mathbb{B})$ when $α\\ge 0$. The results established here directly extend the previous results to the broader setting of complex Banach spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21260",
  "author_total": 3,
  "authors": [
    {
      "name": "Janusz Sokol"
    },
    {
      "name": "Sujoy Majumder"
    },
    {
      "name": "Goutam Halder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nt5x41mf57ps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21260",
  "fulltext_url": null,
  "id": "1nt5x41mf57ps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21260",
  "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": "W7222417870",
  "pdf_url": "https://arxiv.org/pdf/2610.21260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nt5x41mf57ps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Alpha-convex functions in complex Banach spaces",
  "title_text": "Alpha-convex functions in complex Banach spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1nt5x41mf57ps",
  "venue": "arXiv",
  "versions": []
}