1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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        "affiliation": "Istanbul Tech Univ, Dept Math Engn, Maslak, Istanbul, Turkiye", 
        "name": "Zuernaci-Yetis, Fatma"
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      {
        "affiliation": "Dokuz Eylul Univ, Dept Math, Fen Fak, Tinaztepe Kampusu, Buca, Izmir, Turkiye", 
        "name": "Disibuyuk, Cetin"
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    "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>", 
    "doi": "10.1002/mma.10616", 
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      "issue": "5", 
      "pages": "10", 
      "title": "MATHEMATICAL METHODS IN THE APPLIED SCIENCES", 
      "volume": "48"
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    "title": "Generalized Taylor Series and Peano Kernel Theorem"
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