{
  "abstract": "In this paper, we introduce and investigate a parameterized Hankel-type functional $$H_{2,2}^μ(f)=μa_2a_4-a_3^2,\\qquad μ\\in[0,1], $$ which reduces to the classical second-order Hankel determinant $H_{2,2}(f)$ when $μ=1$. We obtain estimates for $H_{2,2}^μ(f)$ over the class of starlike mappings of order $α$ on the unit ball of a complex Banach space and on the unit polydisk $\\mathbb{U}^n$ in $\\mathbb{C}^n$. We also establish estimates for $H_{2,2}^μ(f)$ over the class of quasi-convex mappings of type $B$ on the unit ball of a complex Banach space and on the unit polydisk $\\mathbb{U}^n$. For $μ=1$, our results recover the corresponding estimates for the classical Hankel determinant and extend the known one-dimensional results of Cho et al. \\cite{Cho-2018} and Thomas et al. \\cite{Thomas-Tuneski} to higher-dimensional settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33031",
  "author_total": 4,
  "authors": [
    {
      "name": "Sujoy Majumder"
    },
    {
      "name": "Abhijit Banerjee"
    },
    {
      "name": "Shantanu Panja"
    },
    {
      "name": "Debabrata Pramanik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jer2rk8f0w9a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33031",
  "fulltext_url": null,
  "id": "8jer2rk8f0w9a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33031",
  "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": "W7223874564",
  "pdf_url": "https://arxiv.org/pdf/2610.33031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jer2rk8f0w9a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order $α$ and Quasi-Convex Mappings of Type $B$ in Complex Banach Spaces",
  "title_text": "Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order α and Quasi-Convex Mappings of Type B in Complex Banach Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8jer2rk8f0w9a",
  "venue": "arXiv",
  "versions": []
}