{
  "abstract": "This paper examines the local asymptotic behavior of the distance ‖T(t + ξ(t)) − T(t)‖ near the origin, where (T(t))t>0 is a semigroup on a commutative Banach algebra and ξ : ]0, +∞[ → ]0, +∞[ is a continuous function satisfying lim inft→0+ ξtt>0. Our first main result establishes that if the closed subalgebra A generated by the semigroup (T(t))t>0 is non-unital, then lim supt→0+Tt+ξt−Tt>0. As an application, we derive an exact asymptotic formula for the disk algebra AD¯. Considering the semigroup (T(t))t>0 on AD¯, given by (T(t)f)(z) = f(e−tz) for f∈AD¯, z∈D, and assuming that limt→0+ξtt=γ is finite, we prove that lim supt→0+Tt+ξt−Tt=γ1+γ1+1γ. Furthermore, the closed subalgebra generated by this semigroup is non-unital.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, University of Biskra, BP 145 RP, Biskra 07000, Algeria",
    "Laboratory of Applied Mathematics, Ouargla 30000, Algeria",
    "Department of Mathematics, University of Laghouat, Laghouat 03000, Algeria",
    "Pure and Applied Mathematical Laboratory, Laghouat 03000, Algeria"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Mohamed Agti",
      "orcid": "0009-0008-2526-0104"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Abdelkader Mokhtari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fzmeghbdqpfrm.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203682",
  "fulltext_url": null,
  "id": "fzmeghbdqpfrm",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3682",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7207545887",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/fzmeghbdqpfrm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203682",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Advanced Banach Space Theory",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Asymptotic Behavior of Distance near the Origin Between Two Elements of the Semigroup in a Banach Algebra",
  "title_text": "Asymptotic Behavior of Distance near the Origin Between Two Elements of the Semigroup in a Banach Algebra",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/fzmeghbdqpfrm",
  "venue": "Mathematics",
  "versions": []
}