1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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{
  "@context": "https://schema.org/", 
  "@id": 285649, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Istanbul Tech Univ, Dept Math Engn, Maslak, Istanbul, Turkiye", 
      "name": "Zuernaci-Yetis, Fatma"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Dokuz Eylul Univ, Dept Math, Fen Fak, Tinaztepe Kampusu, Buca, Izmir, Turkiye", 
      "name": "Disibuyuk, Cetin"
    }
  ], 
  "datePublished": "2025-01-01", 
  "description": "<p>As in the polynomial case, non-polynomial divided differences can be viewed as a discrete analog of derivatives. This link between non-polynomial divided differences and derivatives is defined by a generalization of the derivative operator. In this study, we obtain a generalization of Taylor series using the link between non-polynomial divided differences and derivatives, and state generalized Taylor theorem. With the definition of a definite integral, the relation between the non-polynomial divided difference and non-polynomial B-spline functions is given in terms of integration. Also, we derive a general form of the Peano kernel theorem based on a generalized Taylor expansion with the integral remainder. As in the polynomial case, it is shown that the non-polynomial B-splines are in fact the Peano kernels of non-polynomial divided differences.MSC2020 Classification: 65D05, 65D07</p>", 
  "headline": "Generalized Taylor Series and Peano Kernel Theorem", 
  "identifier": 285649, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "Generalized Taylor Series and Peano Kernel Theorem", 
  "url": "https://aperta.ulakbim.gov.tr/record/285649"
}