A GENERALIZATION OF THE PEANO KERNEL AND ITS APPLICATIONS

Based on the q-Taylor Theorem, we introduce a more general form of the Peano kernel (q-Peano) which is also applicable to non-differentiable functions. Then we show that quantum B-splines are the q-Peano kernels of divided differences. We also give applications to polynomial interpolation and construct examples in which classical remainder theory fails whereas q-Peano kernel works

Keywords:

Quantum B-splines, Peano kernel, q-Taylor theorem, divided diğerences quantum derivatives, quantum integrals,

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Current address : Gülter Budakçı: Graduate School of Natural and Applied Sciences,Dokuz Eylül University, Tınaztepe Kampüsü, Buca, 35390 Izmir, Turkey.
E-mail address : gulter.budakci@deu.edu.tr ORCID Address: Current address : Halil Oruç: Department of Mathematics, Faculty of Sciences,Dokuz Eylül University, Tınaztepe Kampüsü, Buca, 35390 Izmir, Turkey.
E-mail address : halil.oruc@deu.edu.tr ORCID Address: http://orcid.org/0000-0002-8262-1892

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

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