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arXiv · 1508.05811

q-Peano Kernel and its Applications

Gülter Budakçı·Halil Oruç
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Abstract

We introduce a q-analogue of the Peano kernel theorem by replacing ordinary derivatives and integrals by quantum derivatives and quantum integrals. In the limit q \to 1, the q-Peano kernel reduces to the classical Peano kernel. We also give applications to polynomial interpolation and construct examples in which classical remainder theory fails whereas q-Peano kernel works. Furthermore we derive a relation between q-B-splines and divided differences via the q-Peano kernel.

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Gülter Budakçı, Halil Oruç. 2015-08-11. q-Peano Kernel and its Applications. https://arxiv.org/abs/1508.05811

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