1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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{
  "DOI": "10.1002/mma.10616", 
  "abstract": "<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>", 
  "author": [
    {
      "family": "Zuernaci-Yetis", 
      "given": " Fatma"
    }, 
    {
      "family": "Disibuyuk", 
      "given": " Cetin"
    }
  ], 
  "container_title": "MATHEMATICAL METHODS IN THE APPLIED SCIENCES", 
  "id": "285649", 
  "issue": "5", 
  "issued": {
    "date-parts": [
      [
        2025, 
        1, 
        1
      ]
    ]
  }, 
  "page": "10", 
  "title": "Generalized Taylor Series and Peano Kernel Theorem", 
  "type": "article-journal", 
  "volume": "48"
}