1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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    <subfield code="a">&lt;p&gt;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&lt;/p&gt;</subfield>
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    <subfield code="a">Generalized Taylor Series and Peano Kernel Theorem</subfield>
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    <subfield code="v">48</subfield>
    <subfield code="p">MATHEMATICAL METHODS IN THE APPLIED SCIENCES</subfield>
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    <subfield code="a">Disibuyuk, Cetin</subfield>
    <subfield code="u">Dokuz Eylul Univ, Dept Math, Fen Fak, Tinaztepe Kampusu, Buca, Izmir, Turkiye</subfield>
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