A GENERALIZATION OF THE PEANO KERNEL AND ITS APPLICATIONS

Year 2018, Volume: 67 Issue: 2, 229 - 241, 01.08.2018

Gülter Budakçı Halil Oruç

Abstract

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 : [e-mail] ORCID Address: Current address : Halil Oruç: Department of Mathematics, Faculty of Sciences,Dokuz Eylül University, Tınaztepe Kampüsü, Buca, 35390 Izmir, Turkey.
• E-mail address : [e-mail] ORCID Address: http://orcid.org/0000-0002-8262-1892