{
  "abstract": "We establish two Korovkin-type approximation theorems for sequences of positive linear operators acting on continuous functions on $[0,\\infty)$. The first result shows that pointwise convergence on all polynomial test functions implies pointwise convergence for every function in the domain that is dominated by a polynomial. The second result provides an analogous criterion for functions of exponential growth, where the test functions are the exponentials $e^{λx}$, $λ\\in\\mathbb{R}$. The results are applied to several classical and modified positive linear operators, including Baskakov, Szász--Mirakjan, Phillips, Post--Widder, Gamma, and Durrmeyer-type operators. Further applications are given to operators associated with modified Bessel functions and hyperbolic functions. The approach provides a unified framework for deriving pointwise convergence on unbounded intervals from convergence on suitable test functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.27517",
  "author_total": 4,
  "authors": [
    {
      "name": "Ulrich Abel"
    },
    {
      "name": "Ana-Maria Acu"
    },
    {
      "name": "Margareta Heilmann"
    },
    {
      "name": "Ioan Rasa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bhpahm8yn0e2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.27517",
  "fulltext_url": null,
  "id": "4bhpahm8yn0e2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.27517",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W7166568041",
  "pdf_url": "https://arxiv.org/pdf/2606.27517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bhpahm8yn0e2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.27517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.27517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Korovkin type theorems for operators acting on functions of polynomial and exponential growth on $[0,\\infty)$",
  "title_text": "Korovkin type theorems for operators acting on functions of polynomial and exponential growth on [0,∞)",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/4bhpahm8yn0e2",
  "venue": "arXiv",
  "versions": []
}