1 Ocak 2025 Dergi makalesi Açık Erişim

Zuernaci-Yetis, Fatma; Disibuyuk, Cetin

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/285649</identifier>
  <creators>
    <creator>
      <creatorName>Zuernaci-Yetis, Fatma</creatorName>
      <givenName>Fatma</givenName>
      <familyName>Zuernaci-Yetis</familyName>
      <affiliation>Istanbul Tech Univ, Dept Math Engn, Maslak, Istanbul, Turkiye</affiliation>
    </creator>
    <creator>
      <creatorName>Disibuyuk, Cetin</creatorName>
      <givenName>Cetin</givenName>
      <familyName>Disibuyuk</familyName>
      <affiliation>Dokuz Eylul Univ, Dept Math, Fen Fak, Tinaztepe Kampusu, Buca, Izmir, Turkiye</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Generalized Taylor Series And Peano Kernel Theorem</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2025</publicationYear>
  <dates>
    <date dateType="Issued">2025-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/285649</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1002/mma.10616</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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  <descriptions>
    <description descriptionType="Abstract">&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;</description>
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