{
  "abstract": "In this paper, we investigate the growth, distortion, pre-Schwarzian and Schwarzian norms of functions in the exponentially convex class \\(\\mathcal C_{e^λ}\\), \\(0<λ\\leπ/2\\), defined by \\(1+zf''(z)/f'(z)\\prec e^{λz}\\). By representing the associated Schwarz function explicitly, we derive parameter-dependent estimates for \\(f\\), \\(f'\\), and the pre-Schwarzian derivative. We further obtain Schwarzian norm estimates under both the general normalization and the additional condition \\(f''(0)=0\\). The corresponding extremal problems are analyzed through suitable Schwarz functions, and the dependence of the resulting bounds on the exponential parameter is made explicit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27563",
  "author_total": 2,
  "authors": [
    {
      "name": "Molla Basir Ahamed"
    },
    {
      "name": "Rajesh Hossain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jwrme62ae7rt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27563",
  "fulltext_url": null,
  "id": "7jwrme62ae7rt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27563",
  "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": "W7214147272",
  "pdf_url": "https://arxiv.org/pdf/2609.27563",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jwrme62ae7rt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27563",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27563"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions",
  "title_text": "Growth, Distortion, and Schwarzian Norm Estimates for Exponentially Convex Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/7jwrme62ae7rt",
  "venue": "arXiv",
  "versions": []
}