1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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  <dc:creator>Zuernaci-Yetis, Fatma</dc:creator>
  <dc:creator>Disibuyuk, Cetin</dc:creator>
  <dc:date>2025-01-01</dc:date>
  <dc:description>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</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/285649</dc:identifier>
  <dc:identifier>oai:aperta.ulakbim.gov.tr:285649</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>MATHEMATICAL METHODS IN THE APPLIED SCIENCES 48(5) 10</dc:source>
  <dc:title>Generalized Taylor Series and Peano Kernel Theorem</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
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